Question 73
Every integer $N$ which is a sum of three perfect squares can obviously be expressed in the form
$$
N = \frac{a^{2} + b^{2} + c^{2} + d^{2}}{1 + abcd}
$$
where $a, b, c, d$ are natural numbers. Is the converse statement true?
$$
N = \frac{a^{2} + b^{2} + c^{2} + d^{2}}{1 + abcd}
$$
where $a, b, c, d$ are natural numbers. Is the converse statement true?