Schinzel circle

Illustration of a Schinzel circle

Schinzel circles are a set of circles with a given number of integer points on the circumference of the circle.

If the number n of points on the circumference of the circle is even, n = 2k, then a Schinzel circle is given by:

${(x-\frac{1}{2})}^2+y^2=\frac{1}{4}{5}^{k-1}$,

whereas for odd n = 2k + 1,

${(x-\frac{1}{3})}^2+y^2=\frac{1}{9}{5}^{2k}$.