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Roots with product 1

Source: 2012 Baltic Way, Problem 4

November 22, 2012
quadraticsalgebraquadratic formulaalgebra unsolved

Problem Statement

Prove that for infinitely many pairs (a,b)(a,b) of integers the equation x2012=ax+bx^{2012} = ax + b has among its solutions two distinct real numbers whose product is 1.
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