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Prove that $F(a_1, ... , a_i)$ contains no $p$th roots of unity not in $F(a_1, ... , a_{i-1})$

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#abstract-algebra #field-theory #prime-numbers #extension-field #roots-of-unity
96
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To prove $\sum_{k=0}^{2016}\frac{1}{2017\zeta_{k}-1}=\frac{2017}{2017^{2017}-1}$

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#number-theory #elementary-number-theory #complex-numbers #summation #roots-of-unity
428
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Extension of map $z\mapsto z^p$

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#abstract-algebra #group-homomorphism #roots-of-unity
563
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How can I calculate all results (3) of a cube root?

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#complex-numbers #roots #roots-of-unity
103
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$ S^2= \left(\sum_{j=0}^{p-1} \epsilon^{j^2}\right)^2$ where $p$ are prime number, $\epsilon $ is primitive p-th root of unity.

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#algebra-precalculus #roots #roots-of-unity #gauss-sums
820
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How to prove that $\cos(\frac{\pi}{13})$ is algebraic and not rational?

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#trigonometry #roots #roots-of-unity
1.3k
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Roots of unity and vandermonde matrix

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#linear-algebra #matrices #algebra-precalculus #roots-of-unity
75
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n-th primitive root of unity

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#roots-of-unity
1k
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Show $\{e^{2\pi ik\sqrt{2}}:k\in\mathbb{Z}\}$ is dense in the unit circle.

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#complex-analysis #roots-of-unity
64
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How to check whether $(x^n - 1)$ is an nth power?

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#elementary-number-theory #roots-of-unity
53
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Cancelling (prime) roots of unity

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#fractions #roots-of-unity
72
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Units of a finite commutative ring

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#abstract-algebra #ring-theory #roots-of-unity
50
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Find double summation

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#polynomials #summation #roots-of-unity #symmetric-polynomials
543
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Sum of powers of roots of unity

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#number-theory #complex-numbers #roots-of-unity
49
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Find the difference between the greatest and smallest among $S(n,k,5)$ for $k=0,1,2,3,4$.

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#binomial-coefficients #fibonacci-numbers #roots-of-unity

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