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• CommentAuthorawllower
• CommentTimeFeb 8th 2011

I have read a post in MO
http://mathoverflow.net/questions/48855/galois-theory-generalization-of-abels-theorem-better-version
The answer says that this transformation can change those two polynomials, but why is it acceptable?? It makes the leading coefficient not 1, doesn't it?
1.
It makes the leading coefficient not 1, but then you just divide by that coefficient to get a polynomial of the desired form, no?
• CommentAuthorawllower
• CommentTimeFeb 8th 2011

But he required that both the leading coefficient and the coefficient of x are 1, didn't him?
2.
in fact they are both 1, since the transformation proposed has the effect of making the leading coefficent and the coefficent of x equal.
3.

The coefficient of \$x^n\$ is \$a^{n/(n - 1)}\$, while that of \$x\$ is \$a * a^{1/(n - 1)} = a^{n/(n - 1)}\$, so in canceling one, you cancel both.

• CommentAuthorvoloch
• CommentTimeFeb 8th 2011

This is not an appropriate discussion for meta. This could have been asked in the comments of the post in question.
• CommentAuthorawllower
• CommentTimeFeb 8th 2011

Well, I didn't have enough reputation points at that time.
And thank you for telling me how the transformation works.
In any case, thank you.