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A135844 Prime numbers p for which the quintic polynomial x^5 - x - 1 modulo p completely factors into linear polynomials. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)