The Perfect Number Theorem and Wilson's Theorem

Marco Riccardi

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 123-128
  • ISSN: 1426-2630

Abstract

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This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! ≅ -1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Φ, proves that Φ is multiplicative and that Σk|n Φ(k) = n.

How to cite

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Marco Riccardi. "The Perfect Number Theorem and Wilson's Theorem." Formalized Mathematics 17.2 (2009): 123-128. <http://eudml.org/doc/267018>.

@article{MarcoRiccardi2009,
abstract = {This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! ≅ -1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Φ, proves that Φ is multiplicative and that Σk|n Φ(k) = n.},
author = {Marco Riccardi},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {123-128},
title = {The Perfect Number Theorem and Wilson's Theorem},
url = {http://eudml.org/doc/267018},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Marco Riccardi
TI - The Perfect Number Theorem and Wilson's Theorem
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 123
EP - 128
AB - This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! ≅ -1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Φ, proves that Φ is multiplicative and that Σk|n Φ(k) = n.
LA - eng
UR - http://eudml.org/doc/267018
ER -

References

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