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Tom De Medts
Tom De Medts
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Let F_q[X]$\mathbb{F}_q[X]$ be the polynomial ring over the finite field with q$q$ elements. Let f$f$ be a polynomial of the form x^n-a$x^n-a$ and let g$g$ be a polynomial of the form x^m-b$x^m-b$. Is it known whether gcd(f,g)$\operatorname{gcd}(f,g)$ is of the same form, i.e. x^k-c$x^k-c$, for some k$k$,c$c$? Thanks in advance.

Let F_q[X] be the polynomial ring over the finite field with q elements. Let f be a polynomial of the form x^n-a and let g be a polynomial of the form x^m-b. Is it known whether gcd(f,g) is of the same form, i.e. x^k-c, for some k,c? Thanks in advance.

Let $\mathbb{F}_q[X]$ be the polynomial ring over the finite field with $q$ elements. Let $f$ be a polynomial of the form $x^n-a$ and let $g$ be a polynomial of the form $x^m-b$. Is it known whether $\operatorname{gcd}(f,g)$ is of the same form, i.e. $x^k-c$, for some $k$,$c$? Thanks in advance.

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Ajdin Halilovic
Ajdin Halilovic
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Gcd of polynomials over a finite field

Let F_q[X] be the polynomial ring over the finite field with q elements. Let f be a polynomial of the form x^n-a and let g be a polynomial of the form x^m-b. Is it known whether gcd(f,g) is of the same form, i.e. x^k-c, for some k,c? Thanks in advance.