Definition:Multiplicative Order of Integer
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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
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