Thread: p,q are prime numbs and a is positive integer

Hi, I am not able to solve this equation. Can anybody help?

(p*q)/(p+q)=((a^2)+1)/(a+1)
"p", "q" are prime numbers and "a" is positive integer

My task is to find all possible pairs of p,q for this equatition.

Thanks in advance!

I've already rewritten that as:
p*q*a - p*a^2 - q*a^2 = -p*q + p + q
and I found that one solution is {p=2,q=2,a=1}

How to find another possible solutions?