Browkin's theorem states that 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 Resource. https://mathworld.wolfram.com/BrowkinsTheorem.html