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%I #10 Dec 06 2016 22:20:09
%S 5101,8161,9631,17921,26681,31091,39161,39671,40151,41491,43331,44171,
%T 44221,48541,75821,77951,84391,94531,109391,111521,113891,114661,
%U 117511,118081,124121,132241,141241,144511,156371,160231,161771,167381,174481,178951,184321,184511,186871,187091,204301
%N Prime numbers p of the form 10k+1 for which the quintic polynomial x^5-x-1 modulus p is factorizable into five binomials.
%C According to class field theory each quintic polynomial is completely reducible mod some prime number p of the form 10k+1.
%D S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, Math. Japonica Vol. 87, No 5 (1992), pp. 883-886.
%H G. C. Greubel, <a href="/A135842/b135842.txt">Table of n, a(n) for n = 1..1000</a>
%t 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
%Y Cf. A135843.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 01 2007
%E Terms a(19) and beyond from _G. C. Greubel_, Dec 06 2016
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