Question 69
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)
$x_n = 5 \cdot 2^n - 1$, $n \in N$. 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)