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The Perfect Number Theorem and Wilson's Theorem

Formalized Mathematics

Volume 17 (2009): Issue 2 (June 2009)

By: Marco Riccardi

Open Access

|Jul 2009

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 Σ_k|n Φ(k) = n.

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Articles in this issue

DOI: https://doi.org/10.2478/v10037-009-0013-y | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 123 - 128

Published on: Jul 14, 2009

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2009 Marco Riccardi, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 17 (2009): Issue 2 (June 2009)