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A106280 Primes p such that the polynomial x^4-x^3-x^2-x-1 mod p has 4 distinct zeros. 3
137, 179, 653, 859, 991, 1279, 1601, 1609, 2089, 2437, 2591, 2693, 2789, 2897, 3701, 3823, 3847, 4451, 4691, 4751, 4919, 5431, 5479, 5807, 5903, 5953, 6203, 6421, 6781, 6917, 7253, 7867, 8317, 9187, 9277, 9533, 9629, 9767, 9907, 9967, 10009, 10079 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This polynomial is the characteristic polynomial of the Fibonacci and Lucas 4-step sequences, A000078 and A073817. The periods of the sequences A000078(k) mod p and A073817(k) mod p have length less than p.

LINKS

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Fibonacci n-Step

MATHEMATICA

t=Table[p=Prime[n]; cnt=0; Do[If[Mod[x^4-x^3-x^2-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 1600}]; Prime[Flatten[Position[t, 4]]]

CROSSREFS

Cf. A106277 (number of distinct zeros of x^4-x^3-x^2-x-1 mod prime(n)), A106296 (period of 4-step sequence mod prime(n)).

Sequence in context: A057879 A179912 A108382 * A139510 A142651 A214265

Adjacent sequences:  A106277 A106278 A106279 * A106281 A106282 A106283

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)