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Digits and divisibility

Source: 2023 Polish Junior Mathematical Olympiad Finals

May 5, 2023
number theory

Problem Statement

Find all pairs of positive integers mm, nn such that the (m+n)(m+n)-digit number 33…3⏟m66…6⏟n\underbrace{33\ldots3}_{m}\underbrace{66\ldots 6}_{n} is a perfect square.
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