DIMACS TR: 93-54

Expressing (a sup 2 + b sup 2 + c sup 2 + d sup 2 ) sup 3 as a Sum of 23 Sixth Powers



Authors: R. H. Hardin and N. J. A. Sloane

ABSTRACT

It is shown that (x sup 1 sup 2 + x sub 2 sup 2 +x sub 3 sup 2 + x sub 4 sup 2 ) sup 3 can be written 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 of 23 points in the four-dimensional unit ball which provide an exact quadrature rule for homogeneous polynomials of degree 6 on S sup 3 . It appears that this result is best possible, i.e. that no 22-term identity exists.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-54.ps
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