On the Equation n1n2= n3n4 Restricted to Factor Closed Sets

作     者：San Ying SHI Michel WEBER 

作者机构：School of Mathematics Hefei University of Technology Hefei 230009 P. R. China IRMA UMR 7501 7 rue Rend Descartes 67084 Strasbourg Cedex France 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第10期

页      面：1517-1530页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by China Scholarship Council 

主　　题：Diophantine equation arithmetical functions factor closed set 

摘      要：We study the number of solutions N（B,F） of the diophantine equation n1n2 = n3n4,where 1 ≤ n1≤B, 1≤ n3 ≤B, n2, n4 ∈ F and F C [1, B] is a factor closed set. We study more particularly the case when F = {m = p1^ε1…pk^εk ,εj∈ {0, 1}, 1≤ j ≤ k}, p1,… ,pk being distinct prime numbers.