OFFSET
1,1
COMMENTS
Apart from 3, subsequence of A003627.
Gives an easily testable condition which allows occasionally to prove the first case of Fermat’s Last Theorem over number fields for a prime number p == 2 mod 3.
LINKS
Alain Kraus, Remarques sur le premier cas du théorème de Fermat sur les corps de nombres, arXiv:1410.0546 [math.NT], 2014, abstract in English.
MATHEMATICA
selQ[p_] := p == 3 || Mod[p, 3] == 2 && AllTrue[Range[(p-3)/2], Mod[1+#^p, p^2] != Mod[(1+#)^p, p^2]&];
Select[Prime[Range[2, 120]], selQ] (* Jean-François Alcover, Sep 26 2018 *)
PROG
(PARI) isok(p) = {if ((p==3) || (p % 3) == 2, for (a=1, (p-3)/2, if (Mod(1+a^p, p^2) == Mod((1+a)^p, p^2), return (0)); ); return (1); ); return (0); }
lista(nn) = forprime(p=3, nn, if (isok(p), print1(p, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 03 2014
STATUS
approved