given odd number e find prime p and q such that ((p-1)*(q-1)-1) is evenly divisible by e
$\displaystyle 2^n-1 $generates prime numbers so we have.
$\displaystyle (2^n-1-1)(2^p-1-1)+1=(2^n-2)(2^p-2)-1=2^{n+p}-2^{p+1}-2^{n+1}+3
$
This what I have though of so far but don't have time to continue so what you can come up with.
So we have $\displaystyle e|2^{n+p}-2(2^{p}+2^{n}-1)+1$. What do you mean be evenly divisible?