Polynomial order

Let P be an irreducible polynomial of degree d≥1 over a prime finite field 𝔽 p. The order of P is the smallest positive integer n such that P(x) 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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