A358147 Primes p such that the polynomial x^7 - 7*x + 3 (mod p) is the product of seven linear factors.

1879, 5381, 5783, 8819, 8893, 12007, 12917, 13967, 14293, 15727, 18311, 20357, 20441, 22639, 26833, 27791, 28711, 31177, 32233, 33829, 35051, 35963, 38167, 40867, 42667, 43003, 46831, 47269, 49937, 51893, 55717, 58603, 59273, 62591, 63487, 64937, 65543, 68881, 72997, 75323, 75659, 75991, 85517

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..43.

Guillaume Duval, Théorème de Chebotarev et Congruences de suites récurrentes linéaires, liens avec les algorithmes de factorisations sur Fp, arXiv:2208.08899 [math.NT], 2022. In French. See page 24.

Wikipedia, Splitting field.

Example

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.

Prog

(PARI) T(x)=x^7-7*x+3;
is(n) = #factor(Mod(1, n)*T(x))~ == 7;
forprime (n=2, 10^6, if(is(n), print1(n, ", ") ) ); \\ Joerg Arndt, Nov 01 2022

Crossrefs

Sequence in context: A045201 A020407 A320719 * A235193 A072494 A260137

Adjacent sequences: A358144 A358145 A358146 * A358148 A358149 A358150

Keyword

nonn

Author

Michel Marcus, Oct 31 2022

Status

approved