de Bruijn's Theorem

A box can be packed with a Harmonic Brick $a\times ab\times abc$ Iff the box has dimensions $ap\times abq\times abcr$ for some natural numbers $p$, $q$, $r$ (i.e., the box is a multiple of the brick).

See also Box-Packing Theorem, Conway Puzzle, Klarner's Theorem

References

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 69-72, 1976.