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Search: id:A135842
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| A135842 |
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Prime numbers p of the form 10k+1 for which quintic polynomial x^5-x-1 modulus p is factorizable into five binomials. |
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6
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| 5101, 8161, 9631, 17921, 26681, 31091, 39161, 39671, 40151, 41491, 43331, 44171, 44221, 48541, 75821, 77951, 84391, 94531
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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According to class field theory each quintic polynomial is completely reducible mod some prime number p of the form 10k+1
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REFERENCES
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S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, Math. Japonica Vol. 87, No 5 (1992), pp. 883-886.
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MATHEMATICA
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a = {}; Do[If[PrimeQ[10n + 1], poly = PolynomialMod[x^5 - x - 1, 10n + 1]; c = FactorList[poly, Modulus -> 10n + 1]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, 10n + 1]]], {n, 1, 10000}]; a
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CROSSREFS
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Cf. A135843.
Sequence in context: A058908 A116887 A034286 this_sequence A025398 A025397 A025402
Adjacent sequences: A135839 A135840 A135841 this_sequence A135843 A135844 A135845
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Dec 01 2007
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