For every positive integer 
, there exists a square in the plane
with exactly 
lattice points in its interior. This was extended by
Schinzel and Kulikowski to all plane figures of a given shape. The generalization
of the square in two-dimensional to the cube
in three dimensions was also proved by Browkin.
Browkin's Theorem
See also
Cube, Schinzel's Theorem, SquareExplore with Wolfram|Alpha
References
Honsberger, R. Mathematical Gems I. Washington, DC: Math. Assoc. Amer., pp. 121-125, 1973.Referenced on Wolfram|Alpha
Browkin's TheoremCite this as:
Weisstein, Eric W. "Browkin's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrowkinsTheorem.html