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.

(In reply to

re: n = 2 by Ady TZIDON)

Ady:

Ah yes, now that I understand, I do agree with your solution for n = 1,2,3,4. Full marks!

Steve