On the Modular Erdös-Burgess Constant

Jun  Hao; Lizhen  Zhang; Haoli  Wang

doi:10.4236/ojdm.2019.91003

Jun Hao¹, Haoli Wang²^*, Lizhen Zhang¹

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.

Keywords: Erdös-Burgess Constant, Davenport Constant, Modular Erdös-Burgess Constant

Cite this paper: Hao, J. , Wang, H. and Zhang, L. (2019) On the Modular Erdös-Burgess Constant. Open Journal of Discrete Mathematics, 9, 11-16. doi: 10.4236/ojdm.2019.91003.

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