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

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

if n is odd or 2k + 1, then

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

^{[1] [2]}

References

1. Weisstein, Eric. "Schinzel Circle". Wolfram MathWorld. Wolfram MathWorld.
2. Mutanguha, Jean Pierre. "Schinzel's Theorem".