Diophantine Equation: solving $x^2-y^2=45$ in integers

Question

How should I solve $x^2-y^2=45$ in integers? I know $$(x+y)(x-y)=3^2\cdot 5,$$ which means $3\mid (x+y)$ or $3\mid (x-y)$, and analogously for $5$.

Answer 1

$$ (x-y)(x+y) = 45 \Rightarrow x + y = \frac{45}{x-y} $$

but since $$ x +y \in \Bbb Z \Rightarrow x - y \mid 45 \Rightarrow (x - y , x + y) \in \{ (45,1) , (1,45) , (-45,-1) , (-1 ,-45) , (3,15) , (5,9) , (-3,-15) , (-5,-9) , (9,5) , (-9, -5) , (15,3) , (-15, - 3) \} $$

so can you get now ?? $$ (x,y) \in ?? $$