On the solutions of a system of two Diophantine equations

查看全文 作　　者：LUO [1,2]JiaGui;YUAN [3]PingZhi

机构地区：[1]School of Mathematics and Information,China West Normal University;[2]School of Mathematics and Information Sciences,Zhaoqing University;[3]School of Mathematics,South China Normal University

出　　处：《Science China Mathematics》索引2014年第57卷第7期,共18页

基　　金：supported by the Guangdong Provincial Natural Science Foundation (Grant Nos.10152606101000000 and S2012040007653);National Natural Science Foundation of China (Grant No.11271142) 摘　　要：We obtain all positive integer solutions(m1,m2,a,b)with a>b,gcd(a,b)=1 to the system of Diophantine equations km21-lat1bt2a2r=C1,km22-lat1bt2b2r=C2,with C1,C2∈{-1,1,-2,2,-4,4},and k,l,t1,t2,r∈Z such that k>0,l>0,r>0,t1>0,t2 0,gcd(k,l)=1,and k is square-free. 关键词：丢番图方程系统正整数解

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On the solutions of a system of two Diophantine equations

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