Calculating points in a circle

Putting this here as I consider my question hypothetical, I don’t actually need the answer per se. So:

Assuming an integer coordinate system, is it possible to calculate all the points that are within a circle of center point P, and radius R?

Couldn’t come up with a solution that didn’t involve brute forcing it, ie getting all the possible points and doing something like

circle.contains(currentPoint);

Any thoughts?