An odd natural number $k$ is given. Consider a composite number $n$. We define $d(n)$ the set of proper divisors of number $n$. If for some number $m$, $d(m)$ is equal to $d(n) \cup \{ k \}$, we call $n$ a good number. prove that there exist only finitely many good numbers. (A proper divisor of a number is any divisor other than one and the number itself.)