If $\zeta_n$ is a primitive $n$th root of unity, why is $\text{dim}_{\Bbb Q}\Bbb Q[\zeta_n]=\phi(n)$?
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
37012
The number of summands $\phi(n)$
18518
Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$
132193
Why $\Bbb Z$ = (integers) is an integral domain?
68458
Roots of unity and large expression
30601
Number of $60$th primitive roots of $-1$
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
16559
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
9787
Primitive roots modulo primes congruent to n!
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
129239
Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
32302
Neukirch’s Number Theory – why is $ℂ \otimes_ℚ K → K_ℂ,~z \otimes a ↦ (j(z)a)_τ$ an isomorphism?
55396
Prove that the class number of $\mathbb{Z}[\zeta_3]$ is $1$
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
61858
Is there $\phi(n)=n/6$
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?