<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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]. </p><p>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].</p></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].

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

Department of Carbohydrate Technology University of Agriculture Krakow, Poland

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

{"article-title":"Fermat\u2019s Little Theorem via Divisibility of Newton\u2019s Binomial"}

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,...

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

Publié en ligne: 30 sept. 2015

Pages: 215 - 229

Reçu: 30 juin 2015

DOI: https://doi.org/10.1515/forma-2015-0018

Mots clés
factorization, primes, Fermat

© by Rafał Ziobro

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

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

Publié en ligne: 30 sept. 2015

Pages: 215 - 229

Reçu: 30 juin 2015

DOI: https://doi.org/10.1515/forma-2015-0018

Mots clésfactorization, primes, Fermat

© by Rafał Ziobro

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Mots clés
factorization, primes, Fermat