If a circle is centered on the origin and has radius r, it may pass through some points with integer coordinates. In fact, by symmetry, this will be a multiple of 4.

Find the smallest radius that will pass through 4n integer points where n=1,2,3,4,5.

Feel free to go further.

Well, now the degree of difficulty is going up.

I expect that radius = 5 is the smallest that goes through 12 points.

It goes through (0,5), (3,4) and (4,3)