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Sums of Squares Formulae With Integer Coefficients
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- Journal:
- Canadian Mathematical Bulletin / Volume 30 / Issue 3 / 01 September 1987
- Published online by Cambridge University Press:
- 20 November 2018, pp. 318-324
- Print publication:
- 01 September 1987
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- Article
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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.
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.