Problem

Source: ELMO 2014, Problem 2, by Matthew Babbitt

Tags: inequalities, induction, number theory, number theory unsolved



Define a beautiful number to be an integer of the form $a^n$, where $a\in\{3,4,5,6\}$ and $n$ is a positive integer. Prove that each integer greater than $2$ can be expressed as the sum of pairwise distinct beautiful numbers. Proposed by Matthew Babbitt