1.1. Find all integer solutions $x$ and $y$ such that

$$
2\left(x^{2}+y^{2}\right)=5(x y+1)
$$
1.1. The equation can be written in the form $(x-2 y)(2 x-y)=5$. We consider the cases:
a) $x-2 y=5,2 x-y=1$; b) $x-2 y=1,2 x-y=5$;

c) $x-2 y=-5,2 x-y=-1$; d) $x-2 y=-1,2 x-y=-5$. The solutions are $(-1,-3),(3,1),(1,3),(-3,-1)$.