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Equation with rational integers and no integers numbers

Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P2 day 1

November 10, 2024
number theorynational olympiad

Problem Statement

Find all pairs (n,q)(n, q) such that nn is a positive integer, qq is a not integer rational and nqāˆ’qn^q-q is an integer.
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