New Concepts of Congruences Modulo 1/n and Positive Integers Modulo 1/n
Habib Lebsir
Habib Lebsir, Cité Salah Boulkeroua Bt8n8-Skikda, Algeria.
Manuscript received on 16 January 2025 | First Revised Manuscript received on 26 January 2025 | Second Revised Manuscript received on 16 March 2025 | Manuscript Accepted on 15 April 2025 | Manuscript published on 30 April 2025 | PP: 11-21 | Volume-5 Issue-1, April 2025 | Retrieval Number: 100.1/ijam.A118805010425 | DOI: 10.54105/ijam.A1188.05010425
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The aim of this article is the creation of new Mathematical beings: The positive integers Modulo 1/n. I hope that they will be used by all the scientific community in general and the computer scientists (cryptographers) particularly. In the other hand, the paper contributes to enlarge the field of number theory and algebraic sets. In this paper, I present a new type of congruences on IN: the congruences modulo n 1 and The Sets of positive integers modulo n 1 denoted respectively ][n 1 and IN 1/n , n E IN*
Keywords: Congruences Modulo, Positive integers Modulo, Integer Part, Partition, Equivalence Classes, Rank, Amplitude, Semi-group.
Scope of the Article: Algebra