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

Rafał Ziobro

Formalized Mathematics (2015)

  • Volume: 23, Issue: 3, page 215-229
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Rafał Ziobro. "Fermat’s Little Theorem via Divisibility of Newton’s Binomial." Formalized Mathematics 23.3 (2015): 215-229. <http://eudml.org/doc/276425>.

@article{RafałZiobro2015,
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].},
author = {Rafał Ziobro},
journal = {Formalized Mathematics},
keywords = {factorization; primes; Fermat},
language = {eng},
number = {3},
pages = {215-229},
title = {Fermat’s Little Theorem via Divisibility of Newton’s Binomial},
url = {http://eudml.org/doc/276425},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Rafał Ziobro
TI - Fermat’s Little Theorem via Divisibility of Newton’s Binomial
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 3
SP - 215
EP - 229
AB - 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].
LA - eng
KW - factorization; primes; Fermat
UR - http://eudml.org/doc/276425
ER -

References

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