Positive integers a,b,c have a common divisor greater than 1
Source: Germany Bundeswettbewerb Mathematik 2008, Round 2, Problem 2
September 7, 2008
inequalitiesnumber theorygreatest common divisorleast common multiplerelatively primenumber theory unsolved
Problem Statement
Let the positive integers chosen such that the quotients \frac{bc}{b\plus{}c}, \frac{ca}{c\plus{}a} and \frac{ab}{a\plus{}b} are integers. Prove that have a common divisor greater than 1.