Prove that for any positive integers $n$ and $k$ there exist positive integers $a>b>c>d>e>k$ such that \[n=\binom{a}{3}\pm\binom{b}{3}\pm\binom{c}{3}\pm\binom{d}{3}\pm\binom{e}{3}\] Radu Ignat
Source: binomial coefficient
Tags: number theory proposed, number theory
Prove that for any positive integers $n$ and $k$ there exist positive integers $a>b>c>d>e>k$ such that \[n=\binom{a}{3}\pm\binom{b}{3}\pm\binom{c}{3}\pm\binom{d}{3}\pm\binom{e}{3}\] Radu Ignat