Prove or disprove $\frac{1}{5}(3-4i)$ is a root of unity.
51314
How to prove that a complex number is not a root of unity?
128060
Proof that the relation $5 \mid (a + 4b)$ is symmetric and transitive
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
128415
Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
32136
How to prove Lucas's Converse of Fermat's Little Theorem without using primitive root?
127129
Using the Argument Principle, evaluate $\int_{|z-i|=7}\frac{z\sinh(z)+3\cosh(z)z}{z\cosh(z)}dz$.
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
111199
Does there exist a formula for product of the primitive $ n $th roots of unity.
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
73454
Prove that $f$ has finite number of roots
55779
How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
147986
Prove: if $|z|=1$ than $\frac{z+1}{z-1}$ is an imaginary number
31076
Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$
116360
Sum of n-th roots of unity