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}

References

↑ Weisstein, Eric. "Schinzel Circle". Wolfram MathWorld. Wolfram MathWorld. Missing or empty |url= (help); |access-date= requires |url= (help)
↑ Mutanguha, Jean Pierre. "Schinzel's Theorem".

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