How many points $(x, y)$ with integer coordinates satisfy the inequality $x^2+y^2 \leq 25$? I had this questions from a previous exam that I couldn't answer, I am apologizing for any English mistakes or for any stupid questions, I tried to solve them and I searched the internet and I couldn't find answers or at least ones with explanations.  
1-if $$x^2 + y^2 \leq 25$$  How many INTEGER pairs of $x,y$ satisfy the inequality?
*I tried to think of combinatorics but I didn't know how it can help me, I had to use brute force in the end.  
Thanks for taking the time to read the question, if anyone has tips for my exam or know any challenging problems I would be really thankful if he/she could tell me about them!
Thanks!

This is not an answer but a comment or a hint (so please don't down-vote it).
Consider this figure:

