Euclidean quadratic forms are ADC forms: A short proof

Abstract

This note presents a short, transparent proof of the theorem that every Euclidean quadratic form over a normed integral domain is an Aubry-Davenport-Cassels form. The theorem, as formulated in the note, allows besides quadratic terms also linear and constant terms, imposes no restrictions on the characteristic of the integral domain, and makes no unnecessary assumptions about the norm.