Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist N4 day2

Tags: number theory, Integers, coprime



Show that there are no triples $(a, b, c)$ of positive integers such that a) $a + c, b + c, a + b$ do not have common multiples in pairs. b)$\frac{c^2}{a + b},\frac{b^2}{a + c},\frac{a^2}{c + b}$ are integer numbers.