Non-gaussian $r-$congruences
General Mathematics
2017-07-05 v1
Abstract
This paper is an invitation to the study and use of general theory of non-gaussian congruences in the theory of numbers. In this work we classify the two kinds of congruences that exist (namely the trivial and non-trivial types) and establish their foundational properties as well as their algebra. Among other results, we show that the consideration of the non-trivial congruences entails the elucidation of a distinguished cyclic subgroup of the permutation group, while the trivial congruences (chief among which is the well-known gaussian congruence) leads to the trivial subgroup. The order of this cyclic group is also computed.
Keywords
Cite
@article{arxiv.1707.00678,
title = {Non-gaussian $r-$congruences},
author = {Olufemi O. Oyadare},
journal= {arXiv preprint arXiv:1707.00678},
year = {2017}
}
Comments
7 pages