A059667 - OEIS

A059667

Primes p such that x^49 = 2 has no solution mod p, but x^7 = 2 has a solution mod p.

4999, 6959, 7351, 11467, 15583, 16073, 20483, 21169, 21757, 30773, 35771, 37339, 38711, 41161, 45179, 46649, 48119, 51157, 51647, 57527, 58997, 64877, 75167, 75853, 80263, 83791, 84869, 85751, 86927, 93983, 95747, 105253, 110251, 115837

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OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..76

MATHEMATICA

Select[Prime[Range[PrimePi[120000]]], ! MemberQ[PowerMod[Range[#], 49, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 7, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 21 2013 *)

PROG

(PARI) forprime(p=2, 116000, x=0; while(x<p&&x^7%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(7^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))

(PARI)

N=10^6; default(primelimit, N);

ok(p, r, k1, k2)={

if ( Mod(r, p)^((p-1)/gcd(k1, p-1))!=1, return(0) );

if ( Mod(r, p)^((p-1)/gcd(k2, p-1))==1, return(0) );

return(1);

}

forprime(p=2, N, if (ok(p, 2, 7, 7^2), print1(p, ", ")));

\\ Joerg Arndt, Sep 21 2012

CROSSREFS