A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x - 1/2)^2 + y^2 = 1/4 5^(k - 1) | for n = 2k even (x - 1/3)^2 + y^2 = 1/9 5^(2k) | for n = 2k + 1 odd. auto right match Note that these solutions do not necessarily have the smallest possible radius. For example, while the Schinzel circle centered at (1/3, 0) and with radius 625/3 has nine lattice points on its circumference, so does the circle centered at (1/3, 0) with radius 65/3. A table of minimal circles to n = 12 is given by Pegg.

circle | circle lattice points | Gauss's circle problem | Kulikowski's theorem | lattice point | Schinzel's theorem | sphere