OFFSET
1,1
COMMENTS
Numbers k, not powers of 5, such that x^4 + x^3 + x^2 + x + 1 factors into four linear polynomials over GF(k).
This sequence consists of numbers of the form p^e where prime p == 1 (mod 5), p^(2e) where prime p == 4 (mod 5) and p^(4e) where prime p == 2, 3 (mod 5),
LINKS
Marius A. Burtea, Table of n, a(n) for n = 1..10000
EXAMPLE
k = 11: in GF(11), x^4 + x^3 + x^2 + x + 1 = (x - 3)*(x - 4)*(x - 5)*(x + 2);
k = 16: let GF(16) = GF(2)[y]/(y^4+y+1), then x^4 + x^3 + x^2 + x + 1 = (x - y^3)*(x - (y^3+y))*(x - (y^3+y^2))*(x - (y^3+y^2+y+1)).
PROG
(PARI) isok(n) = isprimepower(n) && (n%5==1)
(Magma) [n:n in [2..1210]|IsPrimePower(n) and (n mod 5 eq 1)]; // Marius A. Burtea, Sep 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Sep 24 2019
STATUS
approved