English

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 rr-congruences in the theory of numbers. In this work we classify the two kinds of rr-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 rr- congruences entails the elucidation of a distinguished cyclic subgroup of the permutation group, while the trivial rr-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

R2 v1 2026-06-22T20:36:44.240Z