# Tagged: field of characteristic p

## Problem 726

Let $\F$ be a finite field of characteristic $p$.

Prove that the number of elements of $\F$ is $p^n$ for some positive integer $n$.

## Problem 511

Let $F$ be a finite field.
Prove that each element in the field $F$ is the sum of two squares in $F$.

## Problem 91

Show that the matrix $A=\begin{bmatrix} 1 & \alpha\\ 0& 1 \end{bmatrix}$, where $\alpha$ is an element of a field $F$ of characteristic $p>0$ satisfies $A^p=I$ and the matrix is not diagonalizable over $F$ if $\alpha \neq 0$.