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2m | (3n - 2) and 2n | (3m- 2)

Source: 2022 Moldova JBMO TST p11

November 4, 2022
dividesnumber theory

Problem Statement

Find all ordered pairs of positive integers (m,n)(m, n) such that 2m2m divides the number 3n−23n - 2, and 2n2n divides the number 3m−23m - 2.
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