Kulikowski's Theorem
For every Positive Integer 
, there exists a Sphere which has exactly Lattice Points on its surface. The Sphere is given by the equation
where
and 
are the coordinates of the center of the so-called Schinzel Circle 
and
is its Radius.See also Circle Lattice Points, Lattice Point, Schinzel's Theorem
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.
- Destructive Dilemma
- Determinant
- Determinant (Binary Quadratic Form)
- Determinant Expansion by Minors
- Determinant (Knot)
- Determinant Theorem
- Developable Surface
- Deviation
- Devil on Two Sticks
- Devil's Curve
- Devil's Staircase
- Diabolical Cube
- Diabolical Square
- Diabolo
- Diacaustic
- Diagonalization
- Diagonal Matrix
- Diagonal Metric
- Diagonal (Polygon)
- Diagonal (Polyhedron)
- Diagonal Ramsey Number
- Diagonal Slash
- Diagonal (Solidus)
- Diagonals Problem
- Diagram