TITLE:
On the Modular Erdös-Burgess Constant
AUTHORS:
Jun Hao, Haoli Wang, Lizhen Zhang
KEYWORDS:
Erdös-Burgess Constant, Davenport Constant, Modular Erdös-Burgess Constant
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.9 No.1,
December
29,
2018
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 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 n was a prime power or a product of
pairwise distinct primes.