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

1st four --d1 by Ady TZIDON)

I think radius 1 is smaller than sqrt(2).

I do agree with the d1 rating for n = 1.