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Classic number theory, look at the differences

Source: Kazakhstan Nationa Olympiad 2024 (9 grade), P4

March 21, 2024
number theory

Problem Statement

Prove that for any positive integers aa, bb, cc, at least one of the numbers a3b+1a^3b+1, b3c+1b^3c+1, c3a+1c^3a+1 is not divisible by a2+b2+c2a^2+b^2+c^2.
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