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Strange divisibility

Source: Kyiv City MO 2024 Round 1, Problem 10.1

January 28, 2024
number theoryalgebraDivisibility

Problem Statement

Find all pairs of positive integers (a,b)(a, b) such that 4b−14b - 1 is divisible by 3a+13a + 1 and 3a−13a - 1 is divisible by 2b+12b + 1.
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