
TL;DR
This paper generalizes Wilson's theorem to the multiplicative groups of quotient rings of integers in number fields, providing a complete classification of possible product values with simpler proofs.
Contribution
It offers a new, more straightforward proof of a generalization of Wilson's theorem for algebraic number theory contexts.
Findings
Identifies four possible product values for the group elements
Provides necessary and sufficient conditions for each case
Simplifies the proof of the generalization
Abstract
We show that there are four possibilities for the product of all elements in the multiplicative group of a quotient of the ring of integers in a number field, and give precise conditions for each of the possibilities to occur. This generalisation of Wilson's theorem turns out to have been first discovered by M. La\v{s}\v{s}\'ak (2000), but our proof is simpler and more direct.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Identities · Benford’s Law and Fraud Detection · Analytic Number Theory Research
