OFFSET
0,2
COMMENTS
It is known that the sequence of Franel numbers A000172 satisfies the Gauss congruences A000172(n*p^r) == A000172(n*p^(r-1)) (mod p^r) for all primes p and positive integers n and r.
LINKS
F. Beukers, Some congruences for the Apery numbers, Journal of Number Theory, Vol. 21, Issue 2, Oct. 1985, pp. 141-155. local copy
FORMULA
The Gauss congruence a(n*p^r) == a(n(p^(r-1)) (mod p^r) holds for all primes p and positive integers n and r.
Conjecture: the supercongruence a(n*p^r) == a(n(p^(r-1)) (mod p^(2*r)) holds for
all primes p and positive integers n and r.
MAPLE
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, May 05 2023
STATUS
approved