Ukrainian Mathematical Competitions

Let's consider the sequence of positive integers $(x_n)$, that is given by the formula: $x_n=5\cdot 2^n-1$, $n\in N$. Prove, that there is an infinite number of pairs $(x_i,x_j)$ of elements that are mutually-prime, and at the same time none of the elements $x_k$ in this infinite sequence of pairs is included at the initial sequence infinite number of times. (Bogdan Rublyov)