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JBMO 2013 Problem 1

Source: Proposed by Serbia

June 23, 2013
algebrapolynomialVietamodular arithmeticnumber theory proposednumber theoryJBMO

Problem Statement

Find all ordered pairs (a,b)(a,b) of positive integers for which the numbers a3b−1a+1\dfrac{a^3b-1}{a+1} and b3a+1b−1\dfrac{b^3a+1}{b-1} are both positive integers.
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