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Nice diophantine equation.

Source: 2024 Mozambican National MO Selection Test P3

October 2, 2024
ntnumber theoryDiophantine equationfactorizationpositive integersprime numbers

Problem Statement

Find all triples of positive integers (a,b,c)(a,b,c) such that:
a2bc−2ab2c−2abc2+b3c+bc3+2b2c2=11a^2bc-2ab^2c-2abc^2+b^3c+bc^3+2b^2c^2=11
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