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摘要
In the paper we discuss the following type congruences: ((npk)(mpk)) = ((m)(n)) (mod p(r)) where p is a prime, n, m, k and r are various positive integers with n a (c) 3/4 m a (c) 3/4 1, k a (c) 3/4 1 and r a (c) 3/4 1. Given positive integers k and r, denote by W(k, r) the set of all primes p such that the above congruence holds for every pair of integers n a (c) 3/4 m a (c) 3/4 1. Using Ljunggren's and Jacobsthal's type congruences, we establish several characterizations of sets W(k, r) and inclusion relations between them for various values k and r. In particular, we prove that W(k + i, r) = W(k - 1, r) for all k a (c) 3/4 2, i a (c) 3/4 0 and 3 a (c) 1/2 r a (c) 1/2
- 出版日期2012-3
