Schinzel circle

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

Illustration of a Schinzel circle

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

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

whereas for odd n = 2k + 1,

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

[1] [2]

References

1. Weisstein, Eric. "Schinzel Circle". Wolfram MathWorld. Wolfram MathWorld. Retrieved 19 August 2015.
2. Mutanguha, Jean Pierre. "Schinzel's Theorem".