关于Eisenstein数的Terai猜想

摘要

Let (a,b,c) be an Eisenstein triple.It is proved that if 2|ab and c is a prime power,then the equation a2x+axby+b2y=cz has only the positive integer solution (x,y,z)=(1,1,2).%设(a,b,c)是一组Eisenstein数,证明了:当2|ab且c是素数方幂时,方程a2x+axby+b2y=cz仅有正整数解(x,y,z)=(1,1,2).