Newbetuts

Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

Euler's Phi Function Worst Case

Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra

Divisor sum property of Euler phi function with Mobius inversion

How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$

Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$

New identity for Euler's Totient Function?

On Euler phi function

Show that there is no integer n with $\phi(n)$ = 14

Is my shorter expression for $ s_m(n)= 1^m+2^m+3^m+\cdots+(n-1)^m \pmod n$ true?

Show $\sum\limits_{d|n}\phi(d) = n$. [duplicate]

On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $

Proof of Euler's Theorem without abstract algebra?

Iterated Euler's totient function

New posts in totient-function

Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$

Find all positive integers $n$ such that $\phi(n)=6$.

For all $n$ there exists $x$ such that $\varphi(x)<\varphi(x+1)<\ldots<\varphi(x+n)$

$\phi(\pi)$ and other irrationals (Euler's totient function)

Very elementary proof of that Euler's totient function is multiplicative

Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

Euler's Phi Function Worst Case

Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra

Divisor sum property of Euler phi function with Mobius inversion

How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$

Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$

New identity for Euler's Totient Function?

On Euler phi function

Show that there is no integer n with $\phi(n)$ = 14

Is my shorter expression for $ s_m(n)= 1^m+2^m+3^m+\cdots+(n-1)^m \pmod n$ true?

Show $\sum\limits_{d|n}\phi(d) = n$. [duplicate]

On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $

Proof of Euler's Theorem without abstract algebra?

Iterated Euler's totient function