.
Let 
.
Let 
.
Let 
.
![$P(x) \in \mathbb{R}[x]$](http://latex.artofproblemsolving.com/4/5/3/453a624c3b002c1b0e78e0023b24dd22ddd03557.png)
such that:
with 
is an 
th prime and 
is an arbitrary positive integer.
and 
Show that
Where 
denote the number of ordered triples of positive integers 
satisfying![\[
x + yz + zx = n.
\]](http://latex.artofproblemsolving.com/c/d/9/cd97547db7950abad749b1aed29bb288e15dcd53.png)
and 
.
denote the number of positive divisors of 
.
Y by TunarHasanzade, TDVOLIMPTEAM
Find all solutions for the equation 
where 
is a positive integer and 
is a prime.(Don't get mad at me,I've used the search function and did not see a correct and complete solution anywhere.)
where 
is a positive integer and 
is a prime.(Don't get mad at me,I've used the search function and did not see a correct and complete solution anywhere.)
