Definition:Multiplicative Order of Integer

Definition

Let $a$ and $n$ be integers.

Let there exist a positive integer $c$ such that:

$a^c \equiv 1 \pmod n$

Then the least such integer is called the (multiplicative) order of $a$ modulo $n$.

Also see

• Integer has Multiplicative Order Modulo n iff Coprime to n

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): order: 7. (of a modulo $m$)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): order: 7. (of a modulo $m$)

• Weisstein, Eric W. "Multiplicative Order." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MultiplicativeOrder.html