Mathematical Sciences: Composition Laws For Sum Of Square

本项目关注的是 平方和的合成律校长 研究者将确定哪些正整数r，s， 可以写r的平方和乘以a的乘积 s平方和等于n平方和。问题就 用代数、组合学和拓扑学来研究。 本项目涉及的经典研究 二次型这一领域的早期成就之一是 高斯发现，每一个正整数都是 四个正方形的总和。这一领域不仅在纯 数论，但在几何和数学的相对论。

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.