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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 23, Issue 3 (Sep 2015)

Issues

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

Rafał Ziobro
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/forma-2015-0018

Abstract

Solving equations in integers is an important part of the number theory [29]. In many cases it can be conducted by the factorization of equation’s elements, such as the Newton’s binomial. The article introduces several simple formulas, which may facilitate this process. Some of them are taken from relevant books [28], [14].

In the second section of the article, Fermat’s Little Theorem is proved in a classical way, on the basis of divisibility of Newton’s binomial. Although slightly redundant in its content (another proof of the theorem has earlier been included in [12]), the article provides a good example, how the application of registrations could shorten the length of Mizar proofs [9], [17].

Keywords: factorization; primes; Fermat

MSC: 11A51; 11Y55; 03B35

MML identifier:: NEWTON02

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About the article

Received: 2015-06-30

Published Online: 2015-09-30

Published in Print: 2015-09-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2015-0018.

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© by Rafał Ziobro. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. BY-SA 3.0

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