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Equation over Integers

Source: AIME I 2008 Problem 4

March 23, 2008

trigonometryAMCAIMEquadraticsLaTeXspecial factorizationsDiophantine equation

Problem Statement

There exist unique positive integers

x

and

y

that satisfy the equation x^2 \plus{} 84x \plus{} 2008 \equal{} y^2. Find x \plus{} y.