关于Diophantine m-tuples的个数(英文)

On the Number of Diophantine m-tuples

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摘要对于一个由m个正整数构成的数组,若其中任意两个正整数的乘积都等于一个完全平方数减去1,则称这个数组为Diophantine m-tuples.最近,Dujella获得了关于Diophantine2-tuples及3-tuples个数的渐进公式.本文改进了的相关结果. A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square.Recently Dujella derived asymptotic estimates for the number of Diophantine pairs and triples.In this paper we establish some more explicit asymptotic formulas.

作者劳会学

机构地区山东师范大学数学科学学院山东大学数学与系统科学学院

出处《数学进展》 CSCD 北大核心 2010年第3期277-282,共6页 Advances in Mathematics（China）

基金 supported by the NSFC(No.10701048)

关键词 DIOPHANTINE m-tuples 渐进公式除数函数 Diophantine m-tuple asymptotic formula divisor function

分类号 O156.2 [理学—基础数学] O152.5 [理学—基础数学]

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参考文献7

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