Question

求不定解方程(x+y)的平方=x的三次方+y的三次方的正整数解,

Answer 1

（x+y)^2=x^3+y^3

(x+y)^2=(x+y)(x^2-xy+xy^2)

x+y=x^2-xy+y^2

x^2-(y+1)x+y^2-y=0

判别式=(y+1)^2-4(y^2-y)=y^2+2y+1-4y^2+4y=-3y^2+6y+1=4-3(y-1)^2