EXPRESSING (A(2)-POWERS(B(2)+C(2)+D(2))(3) AS A SUM OF 23 6TH)

It is shown that (x(1)(2) + x(2)(2) + X(3)(2) + X(3)(2))3 can be writt en as a sum of 23 sixth powers of linear forms. This is one less than is required in Kempner's 1912 identity. There is a corresponding set o f 23 points in the four-dimensional unit ball which provides an exact quadrature rule for homogeneous polynomials of degree 6 on S-3. It app ears that this result is best possible, i.e., that no 22-term identity exists. (C) 1994 Academic Press, Inc.