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A270802 Primes p of the form 14*k+1 for which there is a solution to x^7 == 2 mod p. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A225390 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

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Last modified January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)