Infinitely many solutions (a,b,c)
Source: Moldova IMO-BMO TST 2003, day 1, problem 4
August 15, 2008
Problem Statement
Prove that the equation \frac {1}{a} \plus{} \frac {1}{b} \plus{} \frac {1}{c}\plus{}\frac{1}{abc} \equal{} \frac {12}{a \plus{} b \plus{} c} has infinitely many solutions in natural numbers.