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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 22:27 EST 2023. Contains 359947 sequences. (Running on oeis4.)