On the Modular Erdös-Burgess Constant - Open Journal of Discrete Mathematics

OJDM > Vol.9 No.1, January 2019

On the Modular Erdös-Burgess Constant ()

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DOI: 10.4236/ojdm.2019.91003 687 Downloads 1,198 Views Citations

Author(s)

Jun Hao¹, Haoli Wang^2*, Lizhen Zhang¹

Affiliation(s)

¹Department of Mathematics, Tianjin Polytechnic University, Tianjin, China.
²College of Computer and Information Engineering, Tianjin Normal University, Tianjin, China.

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

Share and Cite:

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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