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A135843
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Prime numbers p of the form 10k+1 for which pentancacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is factorizable into five binomials.
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5
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691, 8311, 11731, 17291, 25111, 34421, 40531, 41131, 44971, 47521, 51341, 64891, 70111, 74161, 75991, 76261, 86441, 88471, 99611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, Math. Japonica Vol. 87, No 5 (1992), pp. 883-886.
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MATHEMATICA
| a = {}; Do[If[PrimeQ[10n + 1], poly = PolynomialMod[x^5-x^4-x^3-x^2-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
| Cf. A135842.
Sequence in context: A033563 A156036 A029814 * A130662 A029828 A037149
Adjacent sequences: A135840 A135841 A135842 * A135844 A135845 A135846
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 01 2007
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