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Perfect squares as sums or differences of powers

Source: Bundeswettbewerb Mathematik 2020, Round 1 - Problem 1

November 17, 2020
number theorynumber theory proposed

Problem Statement

Show that there are infinitely many perfect squares of the form 50māˆ’50n50^m-50^n, but no perfect square of the form 2020m+2020n2020^m+2020^n, where mm and nn are positive integers.
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