OFFSET
1,1
COMMENTS
For prime p, the quintic residues (mod p) are the positive numbers x = k^5 (mod p) for some k. For primes p = 1 (mod 5), there are (p-1)/5 nonzero quintic residues; for all other primes, there are p-1 nonzero quintic residues. Lehmer states that all primes greater than 3331 have three consecutive nonzero quintic residues.
LINKS
Lehmer D.H., Mechanized mathematics, Bull. Amer. Math. Soc., Vol. 72 (1966), No. 5, 739-759.
MATHEMATICA
ps1=Select[Prime[Range[1000]], Mod[#, 5]==1&]; noConsec={}; Do[r=Union[Table[Mod[n^5, p], {n, p-1}]]; pos=Flatten[Position[Partition[Differences[r, 1], 2, 1], {1, 1}]]; If[pos=={}, AppendTo[noConsec, p]], {p, ps1}]; noConsec
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
T. D. Noe, Mar 29 2011
STATUS
approved