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


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


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


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