# Polynomial order

Let $P$ be an irreducible polynomial of degree $d\ge 1$ over a prime finite field ${𝔽}_{p}$. The order of $P$ is the smallest positive integer $n$ such that $P\left(x\right)$ divides ${x}^{n}-1$. $n$ is also equal to the multiplicative order of any root of $P$. It is a divisor of ${p}_{d}-1$. The polynomial $P$ is a primitive polynomial if $n={p}^{d}-1$.

This tool allows you to enter a polynomial and compute its order. If you enter a reducible polynomial, the orders of all its non-linear factors will be computed and presented.

: over the finite field ${𝔽}_{p}$ of characteristics
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