{"title":"关于模块Erdös-Burgess常量","authors":"Jun Hao, Haoli Wang, Lizhen Zhang","doi":"10.4236/OJDM.2019.91003","DOIUrl":null,"url":null,"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 Erdos-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 Erdos-Burgess constant, in particular, we determined the n-modular Erdos-Burgess constant in the case when n was a prime power or a product of pairwise distinct primes.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the Modular Erdös-Burgess Constant\",\"authors\":\"Jun Hao, Haoli Wang, Lizhen Zhang\",\"doi\":\"10.4236/OJDM.2019.91003\",\"DOIUrl\":null,\"url\":null,\"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 Erdos-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 Erdos-Burgess constant, in particular, we determined the n-modular Erdos-Burgess constant in the case when n was a prime power or a product of pairwise distinct primes.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2019.91003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2019.91003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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 Erdos-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 Erdos-Burgess constant, in particular, we determined the n-modular Erdos-Burgess constant in the case when n was a prime power or a product of pairwise distinct primes.
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