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Prime numbers p for which quintonacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is completely factorizable.

3

`%I #2 Mar 31 2012 10:22:06
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`%S 599,691,733,3163,4259,4397,5419,6637,6733,8009,8311,9803,11731,14923,
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`%T 17291,20627,20873,22777,25111,26339,27947,29339,29389,29527,29917,
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`%U 34123,34421,34739,34757,36527,36809,38783,40433,40531,41131,42859
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`%N Prime numbers p for which quintonacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is completely factorizable.
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`%C A135847 and A135843 are complementary subsets of this sequence.
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`%t a = {}; Do[If[poly = PolynomialMod[x^5-x^4-x^3-x^2-x-1, Prime[n]]; c = FactorList[poly, Modulus -> Prime[n]]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, Prime[n]]], {n, 1, 10000}]; a
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`%Y Cf. A135842, A135843, A135844, A135845, A135847.
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`%K nonn
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`%O 1,1
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`%A _Artur Jasinski_, Dec 01 2007
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