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(a^3 + 1)/( 2ab^2 + 1) is an integer

Source: Switzerland - 2007 Swiss MO Final Round p9

December 26, 2022
number theoryIntegerdividesdivisible

Problem Statement

Find all pairs (a,b)(a, b) of natural numbers such that a3+12ab2+1\frac{a^3 + 1}{2ab^2 + 1} is an integer.
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