MathDB
Simple one!

Source: INMO 1997 Problem 3

October 6, 2005
inequalitiesfunctionalgebra unsolvedalgebra

Problem Statement

If a,b,ca,b,c are three real numbers and a+1b=b+1c=c+1a=t a + \dfrac{1}{b} = b + \dfrac{1}{c} = c + \dfrac{1}{a} = t for some real number tt, prove that abc+t=0.abc + t = 0 .