# A Generalization of the Doubling Construction for Sums of Squares Identities

## TL;DR

This paper generalizes the doubling construction method to generate new sums of squares identities from known solutions, expanding the set of admissible triples using the Hurwitz-Radon function.

## Contribution

It introduces a generalized doubling construction that produces an infinite series of new solutions from any admissible triple, extending previous methods.

## Key findings

- Provides a formula for generating new admissible triples
- Utilizes the Hurwitz-Radon function in the construction
- Expands the set of known sums of squares identities

## Abstract

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize the doubling construction and obtain from any given admissible triple $[r,s,n]$ a series of new ones $[r+\rho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m$, where $\rho$ is the Hurwitz-Radon function.