A358147 - OEIS

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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

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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