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From: pharvey@derwent.co.uk (Paul Harvey)
Newsgroups: sci.math
Subject: IMO problem 2
Date: 4 Aug 2000 15:22:55 -0400
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Does there exist an elegant solution to IMO #2, that is

Let abc = 1, a,b,c are +ve reals

(a-1+1/b)(b-1+1/c)(c-1+1/a)<=1

Only by expanding fully, and arguing several different cases (a>1,
b<1, c<1 etc. ) can I see a solution. 

I expect there's a more elegant way, but I can't see it.

Paul