Fermat

Pierre de Fermat was a French lawyer and amateur mathematician. A number of different mathematical definitions, theorems, conjectures, and methods are named after him.

Mathematics

In number theory

Fermat's little theorem: If $p$ is a prime number and $a$ is an integer that is not a multiple of $p$, then $p$ divides $a^{p-1}-1$.

Primary subject wiki entry: Number:Fermat's little theorem.

Fermat's last theorem: The equation:

$x^{n}+y^{n}=z^{n}$

has no positive integer solutions for $x,y,z,n$ with $n>2$.

Primary subject wiki entry: Number:Fermat's last theorem.

Fermat number: This is a natural number of the form $2^{2^{n}}+1$ where $n$ is a nonnegative integer.

Primary subject wiki entry: Number:Fermat number.

Other subject wiki entries: Groupprops:Fermat number.

Fermat prime: This is a prime number of the form $2^{2^{n}}+1$, where $n$ is a nonnegative integer.

Primary subject wiki entry: Number:Fermat prime.

Other subject wiki entries: Groupprops:Fermat prime.

Fermat pseudoprime: A composite natural number $n$ is termed a Fermat pseudoprime to base $a$, for an integer $a$, if $a$ and $n$ are relatively prime and $a^{n-1}-1$ is a multiple of $n$.

Primary subject wiki entry: Number:Fermat pseudoprime.

In geometry

Fermat point of a triangle: This is defined as the point that minimizes the sum of distances from all the three vertices of the triangle.