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if x^n - 2x = y^n - 2y, then x = y.

Source: 2012 Romania JBMO TST 1.2

June 2, 2020
algebrarationalequation

Problem Statement

Let xx and yy be two rational numbers and nn be an odd positive integer. Prove that, if xn−2x=yn−2yx^n - 2x = y^n - 2y, then x=yx = y.
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