We show how one can use non-prime-power, composite moduli for
computing representations of the product of two $n\times n$ matrices
using only $n^{2+o(1)}$ multiplications.

We consider the following phenomenon: with just one multiplication
we can compute (3u+2v)(3x+2y)= 3ux+4vy mod 6, while computing the same polynomial modulo 5 needs 2 multiplications. We generalize this observation and we define some vectors, called sixtors, with remarkable zero-divisor properties. Using sixtors, we also generalize our earlier result ... more >>>