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Can 44...441 be a perfect square?

Source: Bundeswettbewerb Mathematik 2024, Round 1 - Problem 2

March 8, 2024
number theorynumber theory proposedDigitsPerfect SquaresPerfect Square

Problem Statement

Can a number of the form 44…4144\dots 41, with an odd number of decimal digits 44 followed by a digit 11, be a perfect square?
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