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\frac{1}{a}+ \frac{2}{b} +\frac{3}{c}= 1 find when a is prime and a \le b \le c

Source: CRMO 2012 region 5 p5 Mumbai

September 30, 2018
number theoryDiophantine equationdiophantineprimepositive integers

Problem Statement

Determine with proof all triples (a,b,c)(a, b, c) of positive integers satisfying 1a+2b+3c=1\frac{1}{a}+ \frac{2}{b} +\frac{3}{c} = 1, where aa is a prime number and a≤b≤ca \le b \le c.
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