Does there exist a natural number $n$, for which $n.2^{2^{2014}}-81-n$ is a perfect square?
Problem
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: number theory, Perfect Square
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: number theory, Perfect Square
Does there exist a natural number $n$, for which $n.2^{2^{2014}}-81-n$ is a perfect square?