MathDB

\binom{2014}{m}+\binom{m}{r}=\binom{2014}{r}+\binom{2014-r}{m-r}

Source: INAMO Shortlist 2014 C5

July 13, 2019

combinatoricsBinomial

Problem Statement

Determine all pairs of natural numbers

(m, r)

with

2014 \ge m \ge r \ge 1

that fulfill

\binom{2014}{m}+\binom{m}{r}=\binom{2014}{r}+\binom{2014-r}{m-r}