Values of $p$ such that $p+1$ is perfect square

Question

The only prime $p$ such that $p+1$ is a perfect square is $3$

Which theorem I nee to use?

Answer 1

If $p+1$ is a perfect square, we have $p+1 = n^2$ i.e., $p = n^2-1 = (n+1)(n-1)$.

If $n>2$ then $n-1$ $> 1$ i.e., p is not a prime.

Thus, the only case where $p+1$ can be a perfect square is if $n = 2$ i.e., $p = 3.$