A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 10, 2004, Number 2, Pages 25–33

**Full paper (PDF, 152 Kb)**

## Details

### Authors and affiliations

A. G. Shannon

*Warrane College, The University of New South Wales, Kensington 1465, &
KvB Institute of Technology, 99 Mount Street, North Sydney, NSW 2065, Australia*

### Abstract

This paper looks at some basic number theoretic properties of Fermatian numbers. We define the *n*-th reduced Fermatian number in terms of

so that 1* _{n}* =

*n*, and 1

*! =*

_{n}*n*!, where

*q*! =

_{n}*q*

_{n}q_{n−1}…

*q*

_{1}.

Some congruence properties and relationships with Bernoulli and Fibonacci numbers are explored. Some aspects of the notation and meaning of the Fermatian numbers are also outlined.

### AMS Classification

- 11B65
- 11B39
- 05A30

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## Cite this paper

Shannon, A. G. (2004). Some properties of Fermatian numbers. *Notes on Number Theory and Discrete Mathematics*, 10(2), 25-33.