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arXiv · 2604.24399

A Necessary and Sufficient Condition for Uniqueness of Euclidean Division

Senan Sekhon
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Abstract

A well-known result from the 1960s characterizes all Euclidean domains in which division is guaranteed to produce a unique quotient and remainder. As this relies on the historical (and more restrictive) definition of a Euclidean domain, the question of whether the result still holds under the modern definition was left open. In this paper, we prove the answer is afirmative.

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Senan Sekhon. 2026-04-27. A Necessary and Sufficient Condition for Uniqueness of Euclidean Division. https://arxiv.org/abs/2604.24399

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