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Determine lusophone numbers

Source: Lusophon Mathematical Olympiad 2023 Problem 4

May 27, 2023
algebra

Problem Statement

A positive integer with 3 digits ABC‾\overline{ABC} is LusophonLusophon if ABC‾+CBA‾\overline{ABC}+\overline{CBA} is a perfect square. Find all LusophonLusophon numbers.
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