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May 25, 2007
floor functionIMO Shortlist

Problem Statement

Let α \alpha be the positive root of the equation x^{2} \equal{} 1991x \plus{} 1. For natural numbers m m and n n define m*n \equal{} mn \plus{} \lfloor\alpha m \rfloor \lfloor \alpha n\rfloor. Prove that for all natural numbers p p, q q, and r r, (p*q)*r \equal{} p*(q*r).
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