The concept of k-level for positive integers

Abstract

It is said (cf . [4]) that a positive integer n satisfies property (N) if there exists a representation of n as a sum of 3 squares, n = x1+x2+x3 , with (x 1 ,n) = 1 and x~ < n31 . It has been checked that every positive integer n < 600000, n - 3(mod 8), verifies property (N) .