N4

Part of 2015 Costa Rica - Final Round

Problems(1)

c^2/(a + b),b^2/(a + c),a^2/(c + b) integers, a + c, b + c, a + b coprime

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

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.

number theoryIntegerscoprime