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roots of unity is a subgroup under multiplication

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#group-theory #roots-of-unity
1.1k
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Do the $n$-th roots of unity of an *arbitrary* field form a cyclic group?

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#roots-of-unity
242
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A decomposition on the roots of unity

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#abstract-algebra #complex-numbers #commutative-algebra #roots-of-unity
335
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Square roots of unity modulo a power of a prime

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#finite-groups #modular-arithmetic #roots-of-unity
633
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If $α,β,γ$ belong to ${1,w,w^2}$ then how is number of triplets satisfying $|(aα+bβ+cγ)/(aβ+bγ+cα)| = 1$ equal to $9$?

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#algebra-precalculus #complex-numbers #roots-of-unity
32
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How to find solution to equation A + modinv(A,n) mod n == -1

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#abstract-algebra #finite-groups #modular-arithmetic #inverse #roots-of-unity
323
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Roots of $x^n=0$

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#complex-numbers #roots #roots-of-unity
103
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Let $\alpha_k=1,2,...,10$ be the roots of the unity of order 11, $\alpha_k \neq 1$.

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#linear-algebra #polynomials #roots #roots-of-unity
195
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Sum of $1+4\epsilon +9\epsilon^2 +16\epsilon^3+...+2018^2 \epsilon^{2017}$

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#derivatives #summation #roots-of-unity
430
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Geometric interpretation of the roots of $\left(\frac{z-1}{1+i}\right)^{4} = -1+i$

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#abstract-algebra #algebraic-geometry #complex-numbers #roots #roots-of-unity
867
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discriminant of $x^p-1$

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#abstract-algebra #polynomials #galois-theory #roots-of-unity #discriminant
70
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How can $p^f-p^{f-1}$ divide 2?

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#algebraic-number-theory #extension-field #roots-of-unity
289
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Let $w$ be a primitive root of a unit of order 3, prove that $(1-w+w^2)(1+w-w^2)=4$

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#complex-numbers #roots-of-unity #primitive-roots
77
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Determine the set of complex numbers $z$ such that $z^6$ is a negative real

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#trigonometry #complex-numbers #roots #roots-of-unity
110
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Cyclic units in $Z_p$ towers

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#number-theory #roots-of-unity #cyclotomic-fields

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