MathDB

Let

n

be a positive integer, and let

x

and

y

be a positive real number such that x^n \plus{} y^n \equal{} 1. Prove that \left(\sum^n_{k \equal{} 1} \frac {1 \plus{} x^{2k}}{1 \plus{} x^{4k}} \right) \cdot \left( \sum^n_{k \equal{} 1} \frac {1 \plus{} y^{2k}}{1 \plus{} y^{4k}} \right) < \frac {1}{(1 \minus{} x) \cdot (1 \minus{} y)}.
Author: Juhan Aru, Estonia

Problem Statement