Find all $n$ such that i. $\phi(n)=\frac n2$, ii. $\phi(n)=4$.
117681
For which Natural $n\ge2: \phi(n)=n/2$
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
60284
Infinitely many positive integers $n$ such that $\phi(n) = \frac{n}{4}$?
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
149661
For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
119118
Prove $n\mid \phi(2^n-1)$
119146
How to solve $n < 2^{n/8}$ for $n$?
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
91889
Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?
47790
If $x \geq 2$ prove that $\sum_{ n \leq x} \frac{1}{\phi(n)} = \mathcal{O}(\log(x))$