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Centroamerican 2018, problem 3

Source: 2018 Centroamerican and Caribbean Math Olympiad

June 25, 2018
number theoryCentroamericanprime numbers

Problem Statement

Let x,yx, y be real numbers such that x−y,x2−y2,x3−y3x-y, x^2-y^2, x^3-y^3 are all prime numbers. Prove that x−y=3x-y=3.
EDIT: Problem submitted by Leonel Castillo, Panama.
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