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.
@article{bwmeta1.element.doi-10_2478_v10037-009-0013-y,
author = {Marco Riccardi},
title = {The Perfect Number Theorem and Wilson's Theorem},
journal = {Formalized Mathematics},
volume = {17},
year = {2009},
pages = {123-128},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0013-y}
}
Marco Riccardi. The Perfect Number Theorem and Wilson's Theorem. Formalized Mathematics, Tome 17 (2009) pp. 123-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0013-y/
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