A135844 Prime numbers p for which the quintic polynomial x^5 - x - 1 modulo p completely factors into linear polynomials.

1973, 3769, 5101, 7727, 8161, 9631, 11903, 14629, 16903, 17737, 17921, 18097, 19477, 20747, 20759, 21727, 22717, 23567, 25037, 26681, 27397, 27529, 28279, 29207, 29959, 30497, 31091, 31319, 33289, 36097, 37463, 39161, 39671, 40151, 41491, 42139, 42487, 42689, 43331, 44171, 44221

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

a = {}; Do[poly = PolynomialMod[x^5 - x - 1, Prime[n]]; c = FactorList[poly, Modulus -> Prime[n]]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, Prime[n]]], {n, 1, 10000}]; a

Prog

(PARI) isok(n)=#factormod(x^5-x-1, n)[, 2]==5;
forprime(n=2, 10^6, if(isok(n), print1(n, ", "))); \\ Joerg Arndt, Dec 07 2016

Crossrefs

Cf. A135842, A135843, A135845, A135846, A135847.

Sequence in context: A153352 A251816 A108386 * A135845 A121995 A061998

Adjacent sequences: A135841 A135842 A135843 * A135845 A135846 A135847

Keyword

nonn

Author

Artur Jasinski, Dec 01 2007

Extensions

Terms a(35) and beyond from G. C. Greubel, Dec 06 2016

Status

approved