Let

be a given number greater than 2. We consider the set

of all the integers of the form

with

A number

from

is called indecomposable in

if there are not two numbers

and

from

so that

Prove that there exist a number

that can be expressed as the product of elements indecomposable in

in more than one way. (Expressions which differ only in order of the elements of

will be considered the same.)
%V0
Let $n$ be a given number greater than 2. We consider the set $V_n$ of all the integers of the form $1 + kn$ with $k = 1, 2, \ldots$ A number $m$ from $V_n$ is called indecomposable in $V_n$ if there are not two numbers $p$ and $q$ from $V_n$ so that $m = pq.$ Prove that there exist a number $r \in V_n$ that can be expressed as the product of elements indecomposable in $V_n$ in more than one way. (Expressions which differ only in order of the elements of $V_n$ will be considered the same.)