An integer sum of three fractions
Source: Austrian Math Olympiad 2016, final round, problem 6
May 26, 2016
algebranumber theory
Problem Statement
Let be three integers for which the sum
is integer.
Prove that each of the three numbers
\frac{ab}{c}, \frac{ac}{b}, \frac{bc}{a}
is integer.(Proposed by Gerhard J. Woeginger)