MathNet 1999 — Part 01 Question 15

Let $a$, $b$, $c$ and $d$ be prime numbers such that $a \gt 3b \gt 6c \gt 12d$ and $a^{2} - b^{2} + c^{2} - d^{2} = 1749$. Determine all possible values of $a^{2} + b^{2} + c^{2} + d^{2}$.