In another question I was asking if there are any different $x,y>2$ primes such that $xy+5=a(x+y)$.
Where $a=2^r-1$, and $r>2$.
I was thinking if it is able to find a Pell equation or a similar pattern of $xy+5=a(x+y)$ to say what are and how many integer solutions are there (in particular prime solutions).
Thanks.