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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 17, Issue 2 (Jan 2009)

Issues

The Perfect Number Theorem and Wilson's Theorem

Marco Riccardi
  • Casella Postale 49, 54038 Montignoso, Italy
Published Online: 2009-07-14 | DOI: https://doi.org/10.2478/v10037-009-0013-y

The Perfect Number Theorem and Wilson's Theorem

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.

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About the article


Published Online: 2009-07-14

Published in Print: 2009-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0013-y. Export Citation

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