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On the Modular Erdös-Burgess Constant
Department of Mathematics, Tianjin Polytechnic University, Tianjin, China
College of Computer and Information Engineering, Tianjin Normal University, Tianjin, China
Department of Mathematics, Tianjin Polytechnic University, Tianjin, China
- 1 Department of Mathematics, Tianjin Polytechnic University, Tianjin, China
- 2 College of Computer and Information Engineering, Tianjin Normal University, Tianjin, China
- 3 Department of Mathematics, Tianjin Polytechnic University, Tianjin, China
Open Journal of Discrete Mathematics·Volume 09 (2018)·Pages 11–16·Published 17 December 2018·DOI10.4236/ojdm.2019.91003
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Abstract
Let n be a positive integer. For any integer a , we say that is idempotent modulo n if a 2 ≡a(mod n) . The n -modular Erd ö s-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 Erd ö s-Burgess constant, in particular, we determined the n -modular Erd ö s-Burgess constant in the case when n was a prime power or a product of pairwise distinct primes.
KeywordsErdös-Burgess ConstantDavenport ConstantModular Erdös-Burgess Constant
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