ABOUT ONE APPLICATION OF THE MINKOWSKI THEOREM

Abstract

The article examined as the theoretician-Lagrange's four-squares theorem follows from the geometric Minkowski theorem on a convex body. The proof will use some properties of integer lattices. We will represent consecutive natural numbers in the form of a sum of squares of integers, trying to ensure that in these representations there are as few terms as possible. It can be verified that of the first fifteen natural numbers, only the numbers 7 and 15 are represented as the sum of four squares of integers, the rest can be represented as the sum of less than four squares of integers.