The Perfect Number Theorem and Wilson's Theorem

• Autorzy: Marco Riccardi
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2009
• Tom: 17
• Numer: 2
• Strony: 123-128

Daty

wydano

2009-01-01

online

2009-07-14

Twórcy

autor

Marco Riccardi

• Casella Postale 49, 54038 Montignoso, Italy

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Identyfikatory

DOI

10.2478/v10037-009-0013-y