Question

Find a general formula to express two positive integers which are such that the result obtained by adding their product to the sum of their squares is a perfect square.

Answer 1

Let x,y be integers; then;-

$x^2+xy+y^2=$perfect square$=z^2$$x(x+y)=x^2-y^2$

Putting,$mx=n(z+y),n(x+y)=m(z-y)$

Then, $\frac{x}{2mn+n^2}=\frac{y}{m^2-n^2}=\frac{z}{m^2+mn+n^2}$