Legendre-Teege Reciprocity
History and Overview
2022-05-06 v1
Abstract
Legendre published the first attempted proof of the law of Quadratic Reciprocity. But, in its final form (1797), it had a gap. Some 125 years later Herman Teege published the first rigorous proof of the unproven hypothesis which formed that gap. Then, 48 years later Kenneth Rogers published a second (but implicit) proof. These proofs lifted Legendre's attempt to the list of complete proofs. No detailed exposition of these proofs appears in the literature. Our paper fills that gap.
Cite
@article{arxiv.2205.02372,
title = {Legendre-Teege Reciprocity},
author = {Mark B. Villarino},
journal= {arXiv preprint arXiv:2205.02372},
year = {2022}
}