Revista de la
Unión Matemática Argentina
On the Pythagoras number for polynomials of degree 4 in 5 variables
Santiago Laplagne

Volume 68, no. 1 (2025), pp. 343–348    

Published online (final version): June 30, 2025

https://doi.org/10.33044/revuma.4224

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Abstract

We give an example of a polynomial of degree 4 in 5 variables that is the sum of squares of 8 polynomials and cannot be decomposed as the sum of 7 squares. This improves the current existing lower bound of 7 polynomials for the Pythagoras number $p(5,4)$.

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