On the solutions of a system of two Diophantine equations  

作　　者：LUO JiaGui YUAN 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》2014年第7期1401-1418,共18页中国科学：数学（英文版）

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 ＆gt; 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 ＆gt; 0,l ＆gt; 0,r ＆gt; 0,t1 ＆gt; 0,t2 0,gcd（k,l） = 1,and k is square-free.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：minimal solution fundamental solution Jacobi symbol Diophantine equation 

分 类 号：O156.7[理学—数学] N94[理学—基础数学]