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Q: Find the GCD of the polynomials $x^3 + 4$ and $x^3 + 4x^2 + x +3$ modulo $7$.

The problem I found is that this question doesn't elaborate on modulo or which polynomial to use if both are of equal degree?

As this is for homework, I would prefer working out however as a guidance so please no explicit answer unless added as a spoiler.

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    As for writing in 'math' (the software used here is known as $\TeX$), just put dollar signs around the mathematical expressions in your post.2012-04-19

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$\gcd (f(x),g(x))=\gcd(f(x), g(x)+uf(x))$, where $u$ is any unit. If you subtract one polynomial from the other, the result will be of lower degree. Now you can apply the Euclidean algorithm as you learned it (or as described in the post you linked to).

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    I'm still having a few issues working it out. So, as you said I should do $(x^3 + 4^2 + x +3) - (x^3 + 4) = (4x^2 + x -1)$ However EA is in the form of abc = (a)*(b)+(c)?2012-04-19
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Hint $\rm\ mod\ 7\!:\ c\not\equiv 0\:\Rightarrow\: c^6\equiv 1\:\Rightarrow\: c^3 \equiv\: \pm1 \not\equiv -4,\:$ so $\rm\:x^3+4\:$ is irreducible mod $\rm\ 7$.