关于商高数的Jesmanowicz猜想

The Jesmanowicz conjecture on pythagorean numbers

设u,v是适合u>v,gcd(u,v)=1以及2|uv的正整数.运用初等数论方法讨论了方程(2uv)x+(u2-v2)y=(u2+v2)z的正整数解(x,y,z),证明了当(u,v)≡(1,6),(2,5),(5,2),(6,1)(mod 8)时,该方程仅有正整数解(x,y,z)=(2,2,2).

Let u,v be positive integers such that uv,gcd（u,v）=1 and 2｜uv.In this paper,using some elementary number theory methods,the positive integer solutions（x,y,z） of the equation（2uv）x＋（u2-v2）y=（u2＋v2）z are discussed,and it is proved that if（u,v）≡（1,6）,（2,5）,（5,2） or（6,1）（mod 8）,then the equation has only the positive integer solution（x,y,z）=（2,2,2）.