Problem #PRU-60417

Problems Algebra and arithmetic Algebraic equations and systems of equations

Problem

Show that any natural number \(n\) can be uniquely represented in the form \(n = \binom{x}{1} + \binom{y}{2} + \binom{z}{3}\) where \(x, y, z\) are integers such that \(0 \leq x < y < z\), or \(0 = x = y < z\).