5. Can we claim that the intersection of the set of numbers of the form \(2^{n}-n\) and the set of squares of natural numbers is an empty set? ( \(n>1, n \in N\) )
5. Solution. For \(n=7\) we get: \(2^{7}-7=121=11^{2}\). Therefore, there is at least one value of \(n\) for which the number of the given form is a square of a natural number.