MathDB

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.)

Problem Statement