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Sums of Squares Formulae With Integer Coefficients

Published online by Cambridge University Press:  20 November 2018

Paul Y. H. Yiu
Paul Y. H. Yiu*
Affiliation:
Department of Mathematics University of British Columbia Vancouver, B.C. Canada
*
Current address: Department of Mathematics Ohio State University Columbus, Ohio 43210, USA
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Abstract

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Hidden behind a sums of squares formula are other such formulae not obtainable by restriction. This drastically simplifies the combinatorics involved in the existence problem of sums of squares formulae, and leads to a proof that the product of two sums of 16 squares cannot be rewritten as a sum of 28 squares, if only integer coefficients are permitted. We also construct all [10, 10, 16] formulae.

Keywords

Sums of squares formulaeintercalate matricesstable homotopy classes of spheresnonsingular bilinear mapsHopf-Stiefel conditionPrimary 11E25Secondary 55Q4505B99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 318 - 324
Copyright
Copyright © Canadian Mathematical Society 1987

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