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 Erdös-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
Erdös-Burgess constant, in particular, we determined the n-modular Erdös-Burgess constant in the case when nwas a prime power or a product of
pairwise distinct primes.
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