Documentation

HexGFqMathlib.GeneratorOrder.S0

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theorem HexGFqMathlib.orderOf_gen_2_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_1 Hex.FpPoly.X) = 2 ^ 1 - 1

The Conway generator of GF(2^1) has order 1.

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theorem HexGFqMathlib.orderOf_gen_2_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_2 Hex.FpPoly.X) = 2 ^ 2 - 1

The Conway generator of GF(2^2) has order 3.

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theorem HexGFqMathlib.orderOf_gen_2_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_3 Hex.FpPoly.X) = 2 ^ 3 - 1

The Conway generator of GF(2^3) has order 7.

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theorem HexGFqMathlib.orderOf_gen_2_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_4 Hex.FpPoly.X) = 2 ^ 4 - 1

The Conway generator of GF(2^4) has order 15.

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theorem HexGFqMathlib.orderOf_gen_2_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_5 Hex.FpPoly.X) = 2 ^ 5 - 1

The Conway generator of GF(2^5) has order 31.

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theorem HexGFqMathlib.orderOf_gen_2_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_6 Hex.FpPoly.X) = 2 ^ 6 - 1

The Conway generator of GF(2^6) has order 63.

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theorem HexGFqMathlib.orderOf_gen_2_7 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_7 Hex.FpPoly.X) = 2 ^ 7 - 1

The Conway generator of GF(2^7) has order 127.

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theorem HexGFqMathlib.orderOf_gen_2_8 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_8 Hex.FpPoly.X) = 2 ^ 8 - 1

The Conway generator of GF(2^8) has order 255.

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theorem HexGFqMathlib.orderOf_gen_2_9 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_9 Hex.FpPoly.X) = 2 ^ 9 - 1

The Conway generator of GF(2^9) has order 511.

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theorem HexGFqMathlib.orderOf_gen_2_10 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_10 Hex.FpPoly.X) = 2 ^ 10 - 1

The Conway generator of GF(2^10) has order 1023.

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theorem HexGFqMathlib.orderOf_gen_2_11 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_11 Hex.FpPoly.X) = 2 ^ 11 - 1

The Conway generator of GF(2^11) has order 2047.

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theorem HexGFqMathlib.orderOf_gen_2_12 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_12 Hex.FpPoly.X) = 2 ^ 12 - 1

The Conway generator of GF(2^12) has order 4095.

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theorem HexGFqMathlib.orderOf_gen_2_13 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_13 Hex.FpPoly.X) = 2 ^ 13 - 1

The Conway generator of GF(2^13) has order 8191.

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theorem HexGFqMathlib.orderOf_gen_2_14 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_14 Hex.FpPoly.X) = 2 ^ 14 - 1

The Conway generator of GF(2^14) has order 16383.

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theorem HexGFqMathlib.orderOf_gen_2_15 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_15 Hex.FpPoly.X) = 2 ^ 15 - 1

The Conway generator of GF(2^15) has order 32767.

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theorem HexGFqMathlib.orderOf_gen_2_16 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_2_16 Hex.FpPoly.X) = 2 ^ 16 - 1

The Conway generator of GF(2^16) has order 65535.

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theorem HexGFqMathlib.orderOf_gen_3_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_1 Hex.FpPoly.X) = 3 ^ 1 - 1

The Conway generator of GF(3^1) has order 2.

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theorem HexGFqMathlib.orderOf_gen_3_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_2 Hex.FpPoly.X) = 3 ^ 2 - 1

The Conway generator of GF(3^2) has order 8.

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theorem HexGFqMathlib.orderOf_gen_3_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_3 Hex.FpPoly.X) = 3 ^ 3 - 1

The Conway generator of GF(3^3) has order 26.

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theorem HexGFqMathlib.orderOf_gen_3_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_4 Hex.FpPoly.X) = 3 ^ 4 - 1

The Conway generator of GF(3^4) has order 80.

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theorem HexGFqMathlib.orderOf_gen_3_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_5 Hex.FpPoly.X) = 3 ^ 5 - 1

The Conway generator of GF(3^5) has order 242.

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theorem HexGFqMathlib.orderOf_gen_3_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_6 Hex.FpPoly.X) = 3 ^ 6 - 1

The Conway generator of GF(3^6) has order 728.

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theorem HexGFqMathlib.orderOf_gen_3_7 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_7 Hex.FpPoly.X) = 3 ^ 7 - 1

The Conway generator of GF(3^7) has order 2186.

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theorem HexGFqMathlib.orderOf_gen_3_8 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_3_8 Hex.FpPoly.X) = 3 ^ 8 - 1

The Conway generator of GF(3^8) has order 6560.

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theorem HexGFqMathlib.orderOf_gen_5_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_1 Hex.FpPoly.X) = 5 ^ 1 - 1

The Conway generator of GF(5^1) has order 4.

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theorem HexGFqMathlib.orderOf_gen_5_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_2 Hex.FpPoly.X) = 5 ^ 2 - 1

The Conway generator of GF(5^2) has order 24.

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theorem HexGFqMathlib.orderOf_gen_5_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_3 Hex.FpPoly.X) = 5 ^ 3 - 1

The Conway generator of GF(5^3) has order 124.

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theorem HexGFqMathlib.orderOf_gen_5_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_4 Hex.FpPoly.X) = 5 ^ 4 - 1

The Conway generator of GF(5^4) has order 624.

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theorem HexGFqMathlib.orderOf_gen_5_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_5 Hex.FpPoly.X) = 5 ^ 5 - 1

The Conway generator of GF(5^5) has order 3124.

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theorem HexGFqMathlib.orderOf_gen_5_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_6 Hex.FpPoly.X) = 5 ^ 6 - 1

The Conway generator of GF(5^6) has order 15624.

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theorem HexGFqMathlib.orderOf_gen_5_7 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_7 Hex.FpPoly.X) = 5 ^ 7 - 1

The Conway generator of GF(5^7) has order 78124.

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theorem HexGFqMathlib.orderOf_gen_5_8 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_5_8 Hex.FpPoly.X) = 5 ^ 8 - 1

The Conway generator of GF(5^8) has order 390624.

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theorem HexGFqMathlib.orderOf_gen_7_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_1 Hex.FpPoly.X) = 7 ^ 1 - 1

The Conway generator of GF(7^1) has order 6.

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theorem HexGFqMathlib.orderOf_gen_7_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_2 Hex.FpPoly.X) = 7 ^ 2 - 1

The Conway generator of GF(7^2) has order 48.

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theorem HexGFqMathlib.orderOf_gen_7_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_3 Hex.FpPoly.X) = 7 ^ 3 - 1

The Conway generator of GF(7^3) has order 342.

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theorem HexGFqMathlib.orderOf_gen_7_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_4 Hex.FpPoly.X) = 7 ^ 4 - 1

The Conway generator of GF(7^4) has order 2400.

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theorem HexGFqMathlib.orderOf_gen_7_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_5 Hex.FpPoly.X) = 7 ^ 5 - 1

The Conway generator of GF(7^5) has order 16806.

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theorem HexGFqMathlib.orderOf_gen_7_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_6 Hex.FpPoly.X) = 7 ^ 6 - 1

The Conway generator of GF(7^6) has order 117648.

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theorem HexGFqMathlib.orderOf_gen_7_7 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_7 Hex.FpPoly.X) = 7 ^ 7 - 1

The Conway generator of GF(7^7) has order 823542.

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theorem HexGFqMathlib.orderOf_gen_7_8 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_7_8 Hex.FpPoly.X) = 7 ^ 8 - 1

The Conway generator of GF(7^8) has order 5764800.

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theorem HexGFqMathlib.orderOf_gen_11_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_1 Hex.FpPoly.X) = 11 ^ 1 - 1

The Conway generator of GF(11^1) has order 10.

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theorem HexGFqMathlib.orderOf_gen_11_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_2 Hex.FpPoly.X) = 11 ^ 2 - 1

The Conway generator of GF(11^2) has order 120.

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theorem HexGFqMathlib.orderOf_gen_11_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_3 Hex.FpPoly.X) = 11 ^ 3 - 1

The Conway generator of GF(11^3) has order 1330.

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theorem HexGFqMathlib.orderOf_gen_11_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_4 Hex.FpPoly.X) = 11 ^ 4 - 1

The Conway generator of GF(11^4) has order 14640.

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theorem HexGFqMathlib.orderOf_gen_11_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_5 Hex.FpPoly.X) = 11 ^ 5 - 1

The Conway generator of GF(11^5) has order 161050.

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theorem HexGFqMathlib.orderOf_gen_11_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_11_6 Hex.FpPoly.X) = 11 ^ 6 - 1

The Conway generator of GF(11^6) has order 1771560.

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theorem HexGFqMathlib.orderOf_gen_13_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_1 Hex.FpPoly.X) = 13 ^ 1 - 1

The Conway generator of GF(13^1) has order 12.

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theorem HexGFqMathlib.orderOf_gen_13_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_2 Hex.FpPoly.X) = 13 ^ 2 - 1

The Conway generator of GF(13^2) has order 168.

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theorem HexGFqMathlib.orderOf_gen_13_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_3 Hex.FpPoly.X) = 13 ^ 3 - 1

The Conway generator of GF(13^3) has order 2196.

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theorem HexGFqMathlib.orderOf_gen_13_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_4 Hex.FpPoly.X) = 13 ^ 4 - 1

The Conway generator of GF(13^4) has order 28560.

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theorem HexGFqMathlib.orderOf_gen_13_5 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_5 Hex.FpPoly.X) = 13 ^ 5 - 1

The Conway generator of GF(13^5) has order 371292.

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theorem HexGFqMathlib.orderOf_gen_13_6 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_13_6 Hex.FpPoly.X) = 13 ^ 6 - 1

The Conway generator of GF(13^6) has order 4826808.

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theorem HexGFqMathlib.orderOf_gen_17_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_17_1 Hex.FpPoly.X) = 17 ^ 1 - 1

The Conway generator of GF(17^1) has order 16.

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theorem HexGFqMathlib.orderOf_gen_17_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_17_2 Hex.FpPoly.X) = 17 ^ 2 - 1

The Conway generator of GF(17^2) has order 288.

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theorem HexGFqMathlib.orderOf_gen_17_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_17_3 Hex.FpPoly.X) = 17 ^ 3 - 1

The Conway generator of GF(17^3) has order 4912.

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theorem HexGFqMathlib.orderOf_gen_17_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_17_4 Hex.FpPoly.X) = 17 ^ 4 - 1

The Conway generator of GF(17^4) has order 83520.

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theorem HexGFqMathlib.orderOf_gen_19_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_19_1 Hex.FpPoly.X) = 19 ^ 1 - 1

The Conway generator of GF(19^1) has order 18.

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theorem HexGFqMathlib.orderOf_gen_19_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_19_2 Hex.FpPoly.X) = 19 ^ 2 - 1

The Conway generator of GF(19^2) has order 360.

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theorem HexGFqMathlib.orderOf_gen_19_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_19_3 Hex.FpPoly.X) = 19 ^ 3 - 1

The Conway generator of GF(19^3) has order 6858.

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theorem HexGFqMathlib.orderOf_gen_19_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_19_4 Hex.FpPoly.X) = 19 ^ 4 - 1

The Conway generator of GF(19^4) has order 130320.

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theorem HexGFqMathlib.orderOf_gen_23_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_23_1 Hex.FpPoly.X) = 23 ^ 1 - 1

The Conway generator of GF(23^1) has order 22.

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theorem HexGFqMathlib.orderOf_gen_23_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_23_2 Hex.FpPoly.X) = 23 ^ 2 - 1

The Conway generator of GF(23^2) has order 528.

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theorem HexGFqMathlib.orderOf_gen_23_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_23_3 Hex.FpPoly.X) = 23 ^ 3 - 1

The Conway generator of GF(23^3) has order 12166.

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theorem HexGFqMathlib.orderOf_gen_23_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_23_4 Hex.FpPoly.X) = 23 ^ 4 - 1

The Conway generator of GF(23^4) has order 279840.

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theorem HexGFqMathlib.orderOf_gen_29_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_29_1 Hex.FpPoly.X) = 29 ^ 1 - 1

The Conway generator of GF(29^1) has order 28.

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theorem HexGFqMathlib.orderOf_gen_29_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_29_2 Hex.FpPoly.X) = 29 ^ 2 - 1

The Conway generator of GF(29^2) has order 840.

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theorem HexGFqMathlib.orderOf_gen_29_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_29_3 Hex.FpPoly.X) = 29 ^ 3 - 1

The Conway generator of GF(29^3) has order 24388.

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theorem HexGFqMathlib.orderOf_gen_29_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_29_4 Hex.FpPoly.X) = 29 ^ 4 - 1

The Conway generator of GF(29^4) has order 707280.

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theorem HexGFqMathlib.orderOf_gen_31_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_31_1 Hex.FpPoly.X) = 31 ^ 1 - 1

The Conway generator of GF(31^1) has order 30.

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theorem HexGFqMathlib.orderOf_gen_31_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_31_2 Hex.FpPoly.X) = 31 ^ 2 - 1

The Conway generator of GF(31^2) has order 960.

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theorem HexGFqMathlib.orderOf_gen_31_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_31_3 Hex.FpPoly.X) = 31 ^ 3 - 1

The Conway generator of GF(31^3) has order 29790.

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theorem HexGFqMathlib.orderOf_gen_31_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_31_4 Hex.FpPoly.X) = 31 ^ 4 - 1

The Conway generator of GF(31^4) has order 923520.

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theorem HexGFqMathlib.orderOf_gen_37_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_37_1 Hex.FpPoly.X) = 37 ^ 1 - 1

The Conway generator of GF(37^1) has order 36.

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theorem HexGFqMathlib.orderOf_gen_37_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_37_2 Hex.FpPoly.X) = 37 ^ 2 - 1

The Conway generator of GF(37^2) has order 1368.

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theorem HexGFqMathlib.orderOf_gen_37_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_37_3 Hex.FpPoly.X) = 37 ^ 3 - 1

The Conway generator of GF(37^3) has order 50652.

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theorem HexGFqMathlib.orderOf_gen_37_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_37_4 Hex.FpPoly.X) = 37 ^ 4 - 1

The Conway generator of GF(37^4) has order 1874160.

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theorem HexGFqMathlib.orderOf_gen_41_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_41_1 Hex.FpPoly.X) = 41 ^ 1 - 1

The Conway generator of GF(41^1) has order 40.

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theorem HexGFqMathlib.orderOf_gen_41_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_41_2 Hex.FpPoly.X) = 41 ^ 2 - 1

The Conway generator of GF(41^2) has order 1680.

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theorem HexGFqMathlib.orderOf_gen_41_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_41_3 Hex.FpPoly.X) = 41 ^ 3 - 1

The Conway generator of GF(41^3) has order 68920.

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theorem HexGFqMathlib.orderOf_gen_41_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_41_4 Hex.FpPoly.X) = 41 ^ 4 - 1

The Conway generator of GF(41^4) has order 2825760.

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theorem HexGFqMathlib.orderOf_gen_43_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_43_1 Hex.FpPoly.X) = 43 ^ 1 - 1

The Conway generator of GF(43^1) has order 42.

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theorem HexGFqMathlib.orderOf_gen_43_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_43_2 Hex.FpPoly.X) = 43 ^ 2 - 1

The Conway generator of GF(43^2) has order 1848.

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theorem HexGFqMathlib.orderOf_gen_43_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_43_3 Hex.FpPoly.X) = 43 ^ 3 - 1

The Conway generator of GF(43^3) has order 79506.

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theorem HexGFqMathlib.orderOf_gen_43_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_43_4 Hex.FpPoly.X) = 43 ^ 4 - 1

The Conway generator of GF(43^4) has order 3418800.

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theorem HexGFqMathlib.orderOf_gen_47_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_47_1 Hex.FpPoly.X) = 47 ^ 1 - 1

The Conway generator of GF(47^1) has order 46.

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theorem HexGFqMathlib.orderOf_gen_47_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_47_2 Hex.FpPoly.X) = 47 ^ 2 - 1

The Conway generator of GF(47^2) has order 2208.

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theorem HexGFqMathlib.orderOf_gen_47_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_47_3 Hex.FpPoly.X) = 47 ^ 3 - 1

The Conway generator of GF(47^3) has order 103822.

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theorem HexGFqMathlib.orderOf_gen_47_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_47_4 Hex.FpPoly.X) = 47 ^ 4 - 1

The Conway generator of GF(47^4) has order 4879680.

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theorem HexGFqMathlib.orderOf_gen_53_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_53_1 Hex.FpPoly.X) = 53 ^ 1 - 1

The Conway generator of GF(53^1) has order 52.

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theorem HexGFqMathlib.orderOf_gen_53_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_53_2 Hex.FpPoly.X) = 53 ^ 2 - 1

The Conway generator of GF(53^2) has order 2808.

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theorem HexGFqMathlib.orderOf_gen_53_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_53_3 Hex.FpPoly.X) = 53 ^ 3 - 1

The Conway generator of GF(53^3) has order 148876.

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theorem HexGFqMathlib.orderOf_gen_53_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_53_4 Hex.FpPoly.X) = 53 ^ 4 - 1

The Conway generator of GF(53^4) has order 7890480.

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theorem HexGFqMathlib.orderOf_gen_59_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_59_1 Hex.FpPoly.X) = 59 ^ 1 - 1

The Conway generator of GF(59^1) has order 58.

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theorem HexGFqMathlib.orderOf_gen_59_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_59_2 Hex.FpPoly.X) = 59 ^ 2 - 1

The Conway generator of GF(59^2) has order 3480.

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theorem HexGFqMathlib.orderOf_gen_59_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_59_3 Hex.FpPoly.X) = 59 ^ 3 - 1

The Conway generator of GF(59^3) has order 205378.

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theorem HexGFqMathlib.orderOf_gen_59_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_59_4 Hex.FpPoly.X) = 59 ^ 4 - 1

The Conway generator of GF(59^4) has order 12117360.

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theorem HexGFqMathlib.orderOf_gen_61_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_61_1 Hex.FpPoly.X) = 61 ^ 1 - 1

The Conway generator of GF(61^1) has order 60.

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theorem HexGFqMathlib.orderOf_gen_61_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_61_2 Hex.FpPoly.X) = 61 ^ 2 - 1

The Conway generator of GF(61^2) has order 3720.

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theorem HexGFqMathlib.orderOf_gen_61_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_61_3 Hex.FpPoly.X) = 61 ^ 3 - 1

The Conway generator of GF(61^3) has order 226980.

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theorem HexGFqMathlib.orderOf_gen_61_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_61_4 Hex.FpPoly.X) = 61 ^ 4 - 1

The Conway generator of GF(61^4) has order 13845840.

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theorem HexGFqMathlib.orderOf_gen_67_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_67_1 Hex.FpPoly.X) = 67 ^ 1 - 1

The Conway generator of GF(67^1) has order 66.

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theorem HexGFqMathlib.orderOf_gen_67_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_67_2 Hex.FpPoly.X) = 67 ^ 2 - 1

The Conway generator of GF(67^2) has order 4488.

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theorem HexGFqMathlib.orderOf_gen_67_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_67_3 Hex.FpPoly.X) = 67 ^ 3 - 1

The Conway generator of GF(67^3) has order 300762.

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theorem HexGFqMathlib.orderOf_gen_67_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_67_4 Hex.FpPoly.X) = 67 ^ 4 - 1

The Conway generator of GF(67^4) has order 20151120.

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theorem HexGFqMathlib.orderOf_gen_71_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_71_1 Hex.FpPoly.X) = 71 ^ 1 - 1

The Conway generator of GF(71^1) has order 70.

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theorem HexGFqMathlib.orderOf_gen_71_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_71_2 Hex.FpPoly.X) = 71 ^ 2 - 1

The Conway generator of GF(71^2) has order 5040.

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theorem HexGFqMathlib.orderOf_gen_71_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_71_3 Hex.FpPoly.X) = 71 ^ 3 - 1

The Conway generator of GF(71^3) has order 357910.

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theorem HexGFqMathlib.orderOf_gen_71_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_71_4 Hex.FpPoly.X) = 71 ^ 4 - 1

The Conway generator of GF(71^4) has order 25411680.

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theorem HexGFqMathlib.orderOf_gen_73_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_73_1 Hex.FpPoly.X) = 73 ^ 1 - 1

The Conway generator of GF(73^1) has order 72.

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theorem HexGFqMathlib.orderOf_gen_73_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_73_2 Hex.FpPoly.X) = 73 ^ 2 - 1

The Conway generator of GF(73^2) has order 5328.

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theorem HexGFqMathlib.orderOf_gen_73_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_73_3 Hex.FpPoly.X) = 73 ^ 3 - 1

The Conway generator of GF(73^3) has order 389016.

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theorem HexGFqMathlib.orderOf_gen_73_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_73_4 Hex.FpPoly.X) = 73 ^ 4 - 1

The Conway generator of GF(73^4) has order 28398240.

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theorem HexGFqMathlib.orderOf_gen_79_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_79_1 Hex.FpPoly.X) = 79 ^ 1 - 1

The Conway generator of GF(79^1) has order 78.

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theorem HexGFqMathlib.orderOf_gen_79_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_79_2 Hex.FpPoly.X) = 79 ^ 2 - 1

The Conway generator of GF(79^2) has order 6240.

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theorem HexGFqMathlib.orderOf_gen_79_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_79_3 Hex.FpPoly.X) = 79 ^ 3 - 1

The Conway generator of GF(79^3) has order 493038.

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theorem HexGFqMathlib.orderOf_gen_79_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_79_4 Hex.FpPoly.X) = 79 ^ 4 - 1

The Conway generator of GF(79^4) has order 38950080.

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theorem HexGFqMathlib.orderOf_gen_83_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_83_1 Hex.FpPoly.X) = 83 ^ 1 - 1

The Conway generator of GF(83^1) has order 82.

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theorem HexGFqMathlib.orderOf_gen_83_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_83_2 Hex.FpPoly.X) = 83 ^ 2 - 1

The Conway generator of GF(83^2) has order 6888.

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theorem HexGFqMathlib.orderOf_gen_83_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_83_3 Hex.FpPoly.X) = 83 ^ 3 - 1

The Conway generator of GF(83^3) has order 571786.

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theorem HexGFqMathlib.orderOf_gen_83_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_83_4 Hex.FpPoly.X) = 83 ^ 4 - 1

The Conway generator of GF(83^4) has order 47458320.

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theorem HexGFqMathlib.orderOf_gen_89_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_89_1 Hex.FpPoly.X) = 89 ^ 1 - 1

The Conway generator of GF(89^1) has order 88.

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theorem HexGFqMathlib.orderOf_gen_89_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_89_2 Hex.FpPoly.X) = 89 ^ 2 - 1

The Conway generator of GF(89^2) has order 7920.

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theorem HexGFqMathlib.orderOf_gen_89_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_89_3 Hex.FpPoly.X) = 89 ^ 3 - 1

The Conway generator of GF(89^3) has order 704968.

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theorem HexGFqMathlib.orderOf_gen_89_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_89_4 Hex.FpPoly.X) = 89 ^ 4 - 1

The Conway generator of GF(89^4) has order 62742240.

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theorem HexGFqMathlib.orderOf_gen_97_1 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_97_1 Hex.FpPoly.X) = 97 ^ 1 - 1

The Conway generator of GF(97^1) has order 96.

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theorem HexGFqMathlib.orderOf_gen_97_2 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_97_2 Hex.FpPoly.X) = 97 ^ 2 - 1

The Conway generator of GF(97^2) has order 9408.

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theorem HexGFqMathlib.orderOf_gen_97_3 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_97_3 Hex.FpPoly.X) = 97 ^ 3 - 1

The Conway generator of GF(97^3) has order 912672.

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theorem HexGFqMathlib.orderOf_gen_97_4 :
orderOf (Hex.GFq.ofPoly Hex.Conway.supportedEntry_97_4 Hex.FpPoly.X) = 97 ^ 4 - 1

The Conway generator of GF(97^4) has order 88529280.