<s>[INST] Finding GCD of two polynomials I am finding the GCD ($x^{24}-1, x^{15}-1$) using Euclidean Algorithm. So far I have
EDIT:
$x^{24}-1=x^9(x^{15}-1)$ w remainder $x^9-1$, then $x^{15}=x^6(x^9-1)$ with the remainder $x^6-1$, then $x^9-1=x^3(x^6-1)$ with remainder $X^3-1$, then $x^6-1=x^3(x^3-1)$ with remainder $x^3-1$. Then obviously $x^3-1=1(x^3-1)$ hence our GCD is $x^3-1$.
Thanks everyone for dealing with my dummy moment!
 [/INST] $$x^6-1 = x^3(x^3 -1 ) + x^3 -1$$
$$x^3-1 = 1(x^3-1) + 0$$
$$\gcd{(x^{24}-1, x^{15}-1)}=\gcd{(x^3-1,0)}$$
Therefore, $\gcd{(x^{24}-1, x^{15}-1)}=x^3-1$
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