Question 41
Let $m$ be a positive integer. Show that there exists a positive integer $n$ such that each of the $2m+1$ integers
$$
2^{n}-m, 2^{n}-(m-1), \ldots, 2^{n}+(m-1), 2^{n}+m
$$
is positive and composite.
$$
2^{n}-m, 2^{n}-(m-1), \ldots, 2^{n}+(m-1), 2^{n}+m
$$
is positive and composite.