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Equation on non-negative integers

Source: Brazilian Mathematical Olympiad 2021, Level 3, Problem 5

February 8, 2022
number theoryequationsquaretriplets

Problem Statement

Find all triples of non-negative integers (a,b,c)(a, b, c) such that a2+b2+c2=abc+1.a^{2}+b^{2}+c^{2} = a b c+1.
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