Are there infinitely many solutions to this equation involving primes?

66 Views Asked by At

Consider this equation where $p$ are primes:

$$(p_k)^2+(p_{k+1})^2-1=(p_{k+2})^2$$

A possible solution is given by $p_k=7$, $p_{k+1}=11$ and $p_{k+2}=13$. Do you believe that there are infinitely many solutions? Or plenty of solutions?