On the Modular Erdös-Burgess Constant

Abstract

Let n be a positive integer. For any integer a, we say that is idempotent modulo n if a2≡a(mod n). The n-modular Erdos-Burgess constant is the smallest positive integer l such that any l integers contain one or more integers, whose product is idempotent modulo n. We gave a sharp lower bound of the n-modular Erdos-Burgess constant, in particular, we determined the n-modular Erdos-Burgess constant in the case when n was a prime power or a product of pairwise distinct primes.