Y by Rounak_iitr
Let
be a non-constant polynomial with integer coefficients such that
. For a positive integer
, define
to be the set of positive divisors of
.
A positive integer
is
-cool if there exists a positive integer
for which
Prove that for any such
, there are finitely many
-cool integers.
(The notation
for some set
denotes the set
.)





A positive integer



![$$f[\text{divs}(m)]=\text{divs}(n).$$](http://latex.artofproblemsolving.com/1/2/3/12341f07a9f4396dbced8a380259613f2399b112.png)


(The notation
![$f[S]$](http://latex.artofproblemsolving.com/f/0/1/f01f35bea4da88837806e6056a6e416673778c48.png)

