|
Search: id:A106280
|
|
|
| A106280 |
|
Primes p such that the polynomial x^4-x^3-x^2-x-1 mod p has 4 distinct zeros. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
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: A114645 A057879 A108382 this_sequence A139510 A142651 A142135
Adjacent sequences: A106277 A106278 A106279 this_sequence A106281 A106282 A106283
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), May 02 2005
|
|
|
Search completed in 0.002 seconds
|
