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IMO ShortList 2002, number theory problem 4

Source: IMO ShortList 2002, number theory problem 4

September 28, 2004
algebranumber theoryequationIMO Shortlistinfinitely many solutionsVieta JumpingPell equations

Problem Statement

Is there a positive integer mm such that the equation 1a+1b+1c+1abc=ma+b+c {1\over a}+{1\over b}+{1\over c}+{1\over abc}={m\over a+b+c} has infinitely many solutions in positive integers a,b,ca,b,c?
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