整数的qvolume
古老的知识是，每个非负整数都可以重写为四个平方整数的总和。例如，数字1可以表示为。或者，通常，对于任何非负整数，存在整数使得02+02+02+1202+02+02+120^2+0^2+0^2+1^2nnna,b,c,da,b,c,da,b,c,d n=a2+b2+c2+d2n=a2+b2+c2+d2n = a^2+b^2+c^2+d^2 Joseph-Louis Lagrange proved this in the 1700s and so it is often called Lagrange's Theorem. This is sometimes discussed in relation to quaternions – a type of number discovered by William Hamilton in the 1800s, represented as w+xi+yj+zkw+xi+yj+zkw+x\textbf{i}+y\textbf{j}+z\textbf{k} where w,x,y,zw,x,y,zw,x,y,z are real numbers, and i,ji,j\textbf{i}, \textbf{j} …