# Tagged Questions

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### Polynomial transformation of the roots of another irreducible polynomial.

Suppose I have some monic irreducible polynomial $g(x)$ in $\mathbb{Z}[x]$ with distinct roots $r_1,r_2,\dots,r_n$. Suppose $f(x)$ is some other polynomial, not necessarily irreducible. Is there ...
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### Series of polynomials and uniformly convergence

It's part of the proof of a Lemma of an article I was reading (Algebraic values of transcendental functions at algebraic points). I couldn't understanding one thing: Let f be a complex function such ...
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### Is there a simple procedure to produce algebraic numbers of modulus one that are not roots of unity?

Let $z=e^{i\theta}$ be a complex number of modulus $1$. Trivially if $z$ is a root of unity then $z$ is also an algebraic number, but the converse is known to be false : $z$ can be algebraic without ...
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### Show that $x$ is an algebraic number? Where $x$ is…

Can someone help me with the following problem? Show that $x=\sqrt2+\sqrt[3]3$ is an algebraic number. By finding a polynomial with rational coefficients for which $x$ is a root of. Can someone ...
### Simple formula for integer polynomial with $2\sin(2\pi/n)$ as a root?
Is there a simple formula an integer polynomial that $2\sin(2\pi/n)$ satisfies? For $2\cos(2\pi/n)$ the answer is relatively nice. For any given $n$, we have $2\cos(2\pi/n)= z + z^{-1}$ where \$z = ...