For example, find the gcd of $2x^5 + 4x^3 + 2x^2 + 5x+ 1$ and $x^6 + 3x^5 + 4x^3 + 3x + 1$ in $\mathbb{Z}/7\mathbb{Z}$.
2026-03-29 03:36:36.1774755396
What is the easiest way to find the gcd of two polynomials in the ring $\mathbb{Z}/m\mathbb{Z}$? ($m$ is prime)
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Absolutely the easiest way to find the greatest common divisor of two polynomials in one variable over a finite field (so, $\mathbb Z/p$ only for $p$ prime), is the Euclidean algorithm. It may not seem intuitive, but it is actually a very efficient algorithm.