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Spain Mathematical Olympiad 2007, Problem 5

Source: 2007 Spain Mathematical Olympiad

June 15, 2017
algebranumber theory

Problem Statement

Let a≠1a \neq 1 and be a real positive number and nn be an integer greater than 1.1. Demonstrate that n2<(an+a−n−2)(a+a−1−2).n^2 < \frac{(a^n + a^{-n} -2)}{(a + a^{-1} -2)}.
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