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Impossible divisibility

Source: Romanian TST 3 2008, Problem 3

June 7, 2008
quadraticsmodular arithmeticnumber theoryprime factorizationnumber theory proposed

Problem Statement

Let m, n≥3 m,\ n \geq 3 be positive odd integers. Prove that 2^{m}\minus{}1 doesn't divide 3^{n}\minus{}1.
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