Getting co-ordinates from equation of a circle I am given the question:
How many points with integer coordinates lie on the circumference of circle $x^2 + y^2 = 5^2$
I know the general equation of a circle so the radius is 5. How do I go about it now ?

We want to find the integer solutions of the equation $x^2+y^2=5^2$ .
Observe that we must have $-5\le x,y\le 5$ . WLOG  assume $x\lt y.$
We get : $x^2+x^2\lt x^2+y^2\implies 2x^2 \lt 25 \implies x\le3$
Setting $x=0$ , we get $y = \pm5$.
Setting $x=\pm1$ , we get $y = \pm \sqrt{24}$  , which is not a solution.
Setting $x=\pm2$ , we get $y = \pm \sqrt{21}$ , which is not a solution . 
Setting $x=\pm3$ , we get $y = \pm4$ . 
Now similarly take the case of $y\lt x$ and find all coordinates.
