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A058945
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Coefficients of monic irreducible polynomials over GF(5) listed in lexicographic order.
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13
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10, 11, 12, 13, 14, 102, 103, 111, 112, 123, 124, 133, 134, 141, 142, 1011, 1014, 1021, 1024, 1032, 1033, 1042, 1043, 1101, 1102, 1113, 1114, 1131, 1134, 1141, 1143, 1201, 1203, 1213, 1214, 1222, 1223, 1242, 1244, 1302, 1304, 1311, 1312, 1322, 1323, 1341
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OFFSET
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1,1
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COMMENTS
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Church's table extends through degree 5.
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REFERENCES
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R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, 1983, Table C, pp. 557-560.
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LINKS
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MATHEMATICA
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A058945 = Union[ Reap[ Do[ a = Reverse[ IntegerDigits[n, 5]]; b = {0}; la = Length[a]; k = 1; While[k < la + 1, b = Append[b, a[[k]]*x^(k - 1)]; k++]; b = Plus @@ b; c = Factor[b, Modulus -> 5]; id = IntegerDigits[n, 5]; If[b == c && (id == {1, 0} || id[[-1]] != 0), Sow[ FromDigits[id] ] ], {n, 5, 300}]][[2, 1]]](* Jean-François Alcover, Feb 13 2012, after A058943 *)
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CROSSREFS
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Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, this sequence, A058946. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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