Schinzel Circle
A Circle having a given number of Lattice Points on its Circumference. TheSchinzel circle having 
lattice points is given by the equation
Note that these solutions do not necessarily have the smallest possible Radius. For example, while the Schinzel circlecentered 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.See also Circle, Circle Lattice Points, Kulikowski's Theorem, Lattice Point, Schinzel'sTheorem, Sphere
References
Honsberger, R. ``Circles, Squares, and Lattice Points.'' Ch. 11 in Mathematical Gems I. Washington, DC: Math. Assoc. Amer., pp. 117-127, 1973. Kulikowski, T. ``Sur l'existence d'une sphère passant par un nombre donné aux coordonnées entières.'' L'Enseignement Math. Ser. 2 5, 89-90, 1959. Schinzel, A. ``Sur l'existence d'un cercle passant par un nombre donné de points aux coordonnées entières.'' L'Enseignement Math. Ser. 2 4, 71-72, 1958. Sierpinski, W. ``Sur quelques problèmes concernant les points aux coordonnées entières.'' L'Enseignement Math. Ser. 2 4, 25-31, 1958. Sierpinski, W. ``Sur un problème de H. Steinhaus concernant les ensembles de points sur le plan.'' Fund. Math. 46, 191-194, 1959. Sierpinski, W. A Selection of Problems in the Theory of Numbers. New York: Pergamon Press, 1964.
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