Modular Arithmetic Order Computer
Definition: The order of an integer modulo $n$ is the smallest positive power to which you can raise it to obtain $1$ modulo $n$.
Note: it may not exist (the element $0$ never gives $1$ when raised to any positive power!).
Order Computing Tool
Here’s a tool for computing the orders of elements modulo $n$. Change $n$ and hit evaluate to obtain all orders.
Sage Command Examples
Here’s how you compute the order of an element modulo $n$.
Let’s double check that actually is the order: