Problem

Source: Romania TST 2022

Tags: number theory, Perfect Squares, romania, Romanian TST



Any positive integer $N$ which can be expressed as the sum of three squares can obviously be written as \[N=\frac{a^2+b^2+c^2+d^2}{1+abcd}\]where $a,b,c,d$ are nonnegative integers. Is the mutual assertion true?