Combinatorial Sums ∑_(k≡r) (mod m) (nk)a~k and Lucas Quotients (II)

摘要

This paper is a continuation of [9]. We continue the study of the combinatorial sum We find a different method to deduce new congruences for Lucas quotients of the first family of Lucas sequences considered in [9]. Using these general congruences, one can get some new concrete congruences modulo primes.