CR-MO 2015 N4

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.