Question 121
Determine all prime numbers $p$, for which there exist positive integers $x$ and $y$, such that
$$
\left| \begin{array}{l} p + 49 = 2x^2 \\ p^2 + 49 = 2y^2 \end{array} \right. .
$$
$$
\left| \begin{array}{l} p + 49 = 2x^2 \\ p^2 + 49 = 2y^2 \end{array} \right. .
$$