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A058334

Numbers n such that the trinomial x^n + x + 1 is irreducible over GF(5).

0, 1, 2, 3, 7, 18, 22, 27, 31, 78, 94, 115, 171, 402, 438, 507, 1363, 1467, 2263, 2283, 3627, 9247, 9955

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OFFSET

1,3

COMMENTS

No other n < 4400. - Michael Somos, Mar 12 2007

Next term > 10^4. [Joerg Arndt, Mar 02 2016]

LINKS

PROG

(PARI) isok(n) = polisirreducible(Mod(1, 5)*(x^n + x + 1)); \\ Michel Marcus, Feb 11 2014

(Sage)

P.<x> = GF(5)[]

for n in range(0, 10000):

if (x^n+x+1).is_irreducible():

print(n)

# Joerg Arndt, Mar 02 2016

CROSSREFS

Cf. A002475 (GF(2)), A058857 (GF(7)).

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(1) and a(2) from Eric M. Schmidt, Feb 10 2014

a(22) and a(23) from Joerg Arndt, Mar 02 2016

STATUS

approved