Question 57
Let $a \ge 2$ and $n \ge 3$ be integers. Show that one of the numbers
$$
a^n + 1, a^{n+1} + 1, \dots, a^{2n-2} + 1,
$$
does not share any odd divisor greater than $1$ with any other number in the set.
$$
a^n + 1, a^{n+1} + 1, \dots, a^{2n-2} + 1,
$$
does not share any odd divisor greater than $1$ with any other number in the set.