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 A248173 Primes equal to 3 or congruent to 2 mod 3 that satisfy (1+a^p) == (1+a)^p (mod p^2) for all a between (p-3)/2. 0
 3, 5, 11, 17, 23, 29, 41, 47, 53, 71, 89, 101, 107, 113, 131, 137, 149, 167, 173, 191, 197, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 431, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, 587, 593, 599, 617, 641, 647 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A003627. Sequence in context: A216366 A136084 A045410 * A244029 A106902 A293711 Adjacent sequences:  A248170 A248171 A248172 * A248174 A248175 A248176 KEYWORD nonn AUTHOR Michel Marcus, Oct 03 2014 STATUS approved

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Last modified December 14 05:36 EST 2019. Contains 329978 sequences. (Running on oeis4.)