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Romania TST 2022 Day 2 P4

Source: Romania TST 2022

May 15, 2022
number theoryPerfect SquaresromaniaRomanian TST

Problem Statement

Any positive integer NN which can be expressed as the sum of three squares can obviously be written as N=a2+b2+c2+d21+abcdN=\frac{a^2+b^2+c^2+d^2}{1+abcd}where a,b,c,da,b,c,d are nonnegative integers. Is the mutual assertion true?
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