%I #13 Nov 01 2022 07:12:49

%S 1879,5381,5783,8819,8893,12007,12917,13967,14293,15727,18311,20357,

%T 20441,22639,26833,27791,28711,31177,32233,33829,35051,35963,38167,

%U 40867,42667,43003,46831,47269,49937,51893,55717,58603,59273,62591,63487,64937,65543,68881,72997,75323,75659,75991,85517

%N Primes p such that the polynomial x^7 - 7*x + 3 (mod p) is the product of seven linear factors.

%C Primes p such that GF(p) is a splitting field for the polynomial x^7 - 7*x + 3.

%H Guillaume Duval, <a href="https://arxiv.org/abs/2208.08899">Théorème de Chebotarev et Congruences de suites récurrentes linéaires, liens avec les algorithmes de factorisations sur Fp</a>, arXiv:2208.08899 [math.NT], 2022. In French. See page 24.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Splitting_field">Splitting field</a>.

%e x^7 - 7*x + 3 == (x + 82) * (x + 298) * (x + 407) * (x + 883) * (x + 911) * (x + 1371) * (x + 1685) (mod 1879), so 1879 is a term.

%o (PARI) T(x)=x^7-7*x+3;

%o is(n) = #factor(Mod(1,n)*T(x))~ == 7;

%o forprime (n=2,10^6, if(is(n), print1(n,", ") ) ); \\ _Joerg Arndt_, Nov 01 2022

%K nonn

%O 1,1

%A _Michel Marcus_, Oct 31 2022