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This question is a variation on another one : related question

Let $f(x)$ and $g(x)$ be polynomials with integer coefficients and discriminant of $f(x)$ > discriminant of $g(x)$ , which are irreducible over $\mathbb{Z}$ and have degree $>1$.

It appears that $f(g(x))$ and/or $g(f(x))$ always factors over an extension of degree $p$ where $p$ is the degree of $f(x)$ and/or $g(x)$ , and that extension does not belong to the extension(s) needed for the zero's of $f(g(x))$ resp $g(f(x))$ (*) or their extensions.

(* if you factor $f(g(x))$ its $f(g(x))$ and likewise for the other)

Is that true ? How to (dis)prove this ?

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    Sorry I disagree.2012-09-19

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