A270802 Primes p of the form 14*k+1 for which there is a solution to x^7 == 2 mod p.

631, 673, 953, 1163, 1709, 2003, 2143, 2731, 2857, 3109, 3389, 3739, 4271, 4999, 5237, 5279, 5531, 5867, 6553, 6679, 6959, 7001, 7309, 7351, 7393, 8191, 8681, 9157, 9829, 10627, 10739, 11117, 11243, 11299, 11411, 11467, 13007, 13259, 15121, 15233, 15583, 16073, 18439, 18803, 20063, 20147

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Leonard Eugene Dickson, Cyclotomy and trinomial congruences, Transactions of the American Mathematical Society, 37.3 (1935): 363-380. See page 373.

Maple

ans:=[];
M:=10000;
e:=7; r:=2;
for k from 2 to M do
    p:=ithprime(k);
    if p mod 14 = 1 then
       for x from 2 to p-1 do
          if x^e mod p = r then
             ans:=[op(ans), p];
             break;
          end if;
       end do:
    end if;
end do:
ans;
# Alternative:
select(p -> isprime(p) and numtheory:-mroot(2, 7, p)<>FAIL, [seq(14*i+1, i=1..3000)]); # Robert Israel, Apr 03 2018

Mathematica

Select[Select[14 Range[10^3] + 1, PrimeQ], Function[p, AnyTrue[Range[2, 10^4], Mod[#^7, p] == 2 &]]] (* Michael De Vlieger, Apr 02 2016, Version 10 *)

Prog

(Magma) [p: p in PrimesUpTo(50000) | IsOne(p mod 14) and exists{x: x in ResidueClassRing(p) | x^7 eq 2}]; // Bruno Berselli, Apr 02 2016
(PARI) forprime(p=2, 10^5, if(p%14!=1, next); if(Mod(2, p)^((p-1)/7)==1, print1(p, ", "))); \\ Joerg Arndt, Apr 03 2016

Crossrefs

Cf. A042966.

Sequence in context: A376869 A061163 A045168 * A119504 A020387 A217494

Adjacent sequences: A270799 A270800 A270801 * A270803 A270804 A270805

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2016

Status

approved