%I A135842
%S A135842 5101,8161,9631,17921,26681,31091,39161,39671,40151,41491,43331,44171,
%T A135842 44221,48541,75821,77951,84391,94531
%N A135842 Prime numbers p of the form 10k+1 for which quintic polynomial x^5-x-1 
               modulus p is factorizable into five binomials.
%C A135842 According to class field theory each quintic polynomial is completely 
               reducible mod some prime number p of the form 10k+1
%D A135842 S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, 
               Math. Japonica Vol. 87, No 5 (1992), pp. 883-886.
%t A135842 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 A135842 Cf. A135843.
%Y A135842 Sequence in context: A058908 A116887 A034286 this_sequence A025398 A025397 
               A025402
%Y A135842 Adjacent sequences: A135839 A135840 A135841 this_sequence A135843 A135844 
               A135845
%K A135842 nonn
%O A135842 1,1
%A A135842 Artur Jasinski (grafix(AT)csl.pl), Dec 01 2007