关于丢番图方程x(x+1)(x+2)=2p^ky^n的解

On the Diophantine equation x(x+1)(x+2)=2p^ky^n

设p是奇素数,利用初等方法证明了:当k≥2,n>2,且都是整数,则丢番图方程x(x+1)(x+2)=2pKyn没有正整数解(p,x,y).

Let p be odd prime. This paper uses the elementary method to study the problem that ifk≥2,n〉2, are integers, Diophantine equation x（x＋1）（x＋2）=2p^ky^n has no positive integer solution.