## Tags » Theorem

#### Wilsons Theorem

Wisons Theorem says, that p is prime if and only if (p-1)!+1 is a multiple of p.

To prove this, we must show, that if (p-1)!+1 is a multiple of p, that then p is prime and that if p is prime, that then (p-1)!+1 is a multiple of p. 274 more words

#### Maximum Modulus Principle

Theorem. Let the function  be analytic and not constant in a given domain . Then has no maximum value in . That is, there’s no point in the domain such that… 146 more words

Theorem

#### First Isomorphism Theorem

Theorem. Let be an epimorphism (of groups). Then

Proof. To show that and are isomorphic, I need to show that there exists a function from to which is, first of all, a homomorphism. 72 more words

Theorem

#### Liouville's Theorem

Theorem. If a function is entire and bounded in the complex plane, then is constant throughout the plane.

Proof. From the assumptions, is bounded. So… 119 more words

Theorem

#### A Set of Conjectures: Sequels to Fermat's Last Theorem?

This story began yesterday, with this blog-post: http://robertlovespi.wordpress.com/2014/12/10/pythagorean-and-fermatian-triples-and-quadruples/ — but it hasn’t ended there. When discussing this with my wife (who, like myself, is also a teacher of mathematics) while writing that post, she speculated that more interesting things might happen — such as a “no solutions” situation, as is the case with Fermat’s Last Theorem — with a search for a Fermatian quadruple, if the exponent used were larger than three, the exponent I checked yesterday. 496 more words

Mathematics

Progressive

Electronic