Question 149
Prove that for any given positive integer $k$, there exist infinitely many positive integers $n$, such that the numbers
$$
2^n + 3^n - 1, 2^n + 3^n - 2, \dots, 2^n + 3^n - k
$$
are all composite.
$$
2^n + 3^n - 1, 2^n + 3^n - 2, \dots, 2^n + 3^n - k
$$
are all composite.