...e2 + £2 + r\2 + 62, so the multiplicative property of absolute value gives an identity expressing the product of two sums of eight squares as a sum of eight squares. After discovering this, Graves searched the literature for such identities, and uncovered Euler's four-square...

...the output for u * v combined with the fact that Q(uv) = Q(u)Q(v) provides an explicit expression of the product of two sums of eight squares as a sum of eight squares. > Q := func< x \ lnnerProduct(x,x) >; > Q(u). Q(u*v) eq Q(u)*Q(v); ul~2 + u2~2 + u3~2 + u4~2 + u5~2...