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number theory, divisibility, inequality

Source: BMO 2024 Problem 3

April 29, 2024

number theoryDivisibilityInequalityinequalities

Problem Statement

Let

a

and

b

be distinct positive integers such that

3^a + 2

is divisible by

3^b + 2

. Prove that

a > b^2

.
Proposed by Tynyshbek Anuarbekov, Kazakhstan

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