Solve the following Diophantine equation

Question

I need help with solving the following diophantine equation: $$x^2+y^2=2018$$

Thanks a lot in advance!

Answer 1

HINTS:

$$2(31^2)<2018<2(32^2)$$ $$44^2<2018<45^2$$

Use these two to narrow down the range of possibilities, and test them by assigning all $y$ and seeing if $2018-y^2$ is a square number.