题目

求不定方程：(x+y)^2=x^3+y^3的正整数解

提问时间：2020-11-23

答案

(x+y)^2=x^3+y^3=(x+y)(x^2-xy+y^2)则：(x+y)(x^2-xy+y^2-x-y)=0,由x,y是正整数,则:x+y>0则：x^2-xy+y^2-x-y=0整理得:(x+y)(x+y-1)=3xy由x,y都是正整数,则：3|(x+y)(x+y-1)于是：x+y≄3k-1(k是正整数)(否则,x+y...