Inspired by Aditya Kumar

Number Theory Level 5

$\large \dfrac{x+y}{x^2+y^2} =\dfrac1{10}$

Find the number of pairs of integers $(x,y)$ that satisfy the equation above.

1 solution

Tran Hieu
Mar 26, 2016

From the equation we could have $(x-5)^{2} + (y-5)^{2} = 50$

So we could have $[(x-5)^{2};(y-5)^{2}] = [1;49] or [49;1] or [25;25]$

Each of the above could generate 4 pair of (x,y) but for the last one we have (0,0) pair that need to remove. So total we have $\boxed{11}$ pairs.