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diophantine (c-1) (ab- b -a) = a + b-2

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 Shortlist N2

October 1, 2021
number theorydiophantineDiophantine equation

Problem Statement

Determine all triples (a,b,c)(a, b, c) of nonnegative integers that satisfy: (c−1)(ab−b−a)=a+b−2(c-1) (ab- b -a) = a + b-2
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