Number theory · Divisibility · Prime factorisation · Squares · Counting unit cubes
The edge of a wooden cube is a natural number \(a > 2\). The cube is painted all over and then cut into unit cubes. It turns out that the number of unit cubes with exactly two painted faces divides the number of unit cubes with no painted face at all. Find the smallest value of \(a\) for which this can happen.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2007, 1. letnik, category A, problem 5. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source