OFFSET
1,1
COMMENTS
According to class field theory each quintic polynomial is completely reducible mod some prime number p of the form 10k+1.
REFERENCES
S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, Math. Japonica Vol. 87, No 5 (1992), pp. 883-886.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 01 2007
EXTENSIONS
Terms a(19) and beyond from G. C. Greubel, Dec 06 2016
STATUS
approved