Mathematical Sciences: Composition Laws For Sum Of Square

这个项目是关于平方和的合成律的存在性。首席调查员将确定对哪个正整数r、S和n，可以将r平方和乘以S平方和的乘积写成n平方和。这个问题将用代数、组合学和拓扑学来解决。本课题与二次型的经典研究有关。这一领域最早的成就之一是高斯发现每个正整数都是四个平方的和。这一领域不仅在纯数理论中很重要，而且在几何学和相对论数学中也很重要。

This project is concerned with the existence of composition laws for sums of squares. The principal investigator will determine for which positive integers r,s, and n one can write the product of a sum of r squares times a sum of s squares as a sum of n squares. The problem will be approached using algebra, combinatorics and topology. This project is related to the classical study of quadratic forms. One of the early acheivements in this field is the discovery by Gauss that every positive whole number is the sum of four squares. This area is important not only in pure number theory but in geometry and the mathematics of relativity.