If $x,y$ are integers greater than $1$ and $n$ is a positive integer such that $2^n + 1=xy$ , $\exists 1< aIf $x,y$ are integers greater than $1$ and $n$ is a positive integer such that $2^n + 1=xy$ , then is it true that either $2^n|x-1$ or $2^n|y-1$ ?  I have only been able to observe that both $x,y$ are odd . Please help  
EDIT : As is seen from an answer : the original claim does not hold ; so I ask does there exist $a>1 , a<n$  such that $2^a|x-1$ or $2^a|y-1$ ?

Let $x=2^{a+p}c+1,y=2^ad+1$ where $p\ge0$ and $c,d$ are add
$2^n+1=xy=2^{2a+p}cd+2^{a+p}c+2^ad+1$
$\iff2^n=2^a(2^{a+p}cd+2^pc+d)$
$\iff2^{n-a}-[2^{a+p}cd+2^pc]=d$ which is odd
If $p>0,2^{n-a}-[2^{a+p}cd+2^pc]$ is even 
$\implies p=0\implies$ the highest power of $2$ that divides  $x-1$ and $y-1$  will be the same
