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Smallest value of |253^m - 40^n|

Source: Kyiv City MO 2024 Round 1, Problem 9.5

January 28, 2024
number theoryDiophantine equation

Problem Statement

Find the smallest value of the expression ∣253m−40n∣|253^m - 40^n| over all pairs of positive integers (m,n)(m, n).
Proposed by Oleksii Masalitin
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