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Found problems: 1

2013 Gheorghe Vranceanu, 2
Tags: grade 2 , number theory
Given two natural numbers $ n\ge 2,a, $ prove that there exists another natural number $ v\ge 2 $ such that: $$ \frac{v+\sqrt{v^2-4}}{2} =\left( \frac{n+\sqrt{n^2-4}}{2} \right)^a $$