List questions from totient-function

Published on 04 Apr 2012 - 15:08

436

Views

How to show $\varphi (ab) = d\varphi(a)\varphi(b) / \varphi(d) $?

Published on 16 Apr 2012 - 12:45

329

Views

How to prove $n*\varphi(n)/2 $ sum?

Published on 16 Apr 2012 - 14:38

689

Views

Factoring a number $p^a q^b$ knowing its totient

Published on 12 May 2012 - 11:56

11.6k

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Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$

Published on 17 Jun 2012 - 9:51

396

Views

Sum of floor function $\pmod{n}$

Published on 01 Jul 2012 - 4:42

11.2k

Views

Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them

Published on 30 Mar 2026 - 3:23

1.3k

Views

Problem on Euler's Phi function

Published on 08 Jul 2012 - 6:14

520

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Working with phi function with larger numbers?

Published on 14 Jul 2012 - 6:10

6.4k

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$\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k

Published on 17 Jul 2012 - 2:41

131

Views

Minimal $x$ for which $\phi(k) > n$ for all $k > x$

Published on 28 Mar 2026 - 8:49

1.1k

Views

Updates on Lehmer's Totient Problem

Published on 22 Jul 2012 - 16:43

445

Views

Solving $\phi (n) < (n-1) \cdot \frac{15499}{94744} $

Published on 25 Mar 2026 - 17:45

742

Views

Solutions of $\phi(x)=n$ for a given n.

Published on 12 Aug 2012 - 11:47

209

Views

One problem with Euler's function

Published on 16 Aug 2012 - 9:31

List Question

If $n=2\phi(n)$, then $n=2^j$.

How to show $\varphi (ab) = d\varphi(a)\varphi(b) / \varphi(d) $?

How to prove $n*\varphi(n)/2 $ sum?

Factoring a number $p^a q^b$ knowing its totient

Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$

Sum of floor function $\pmod{n}$

Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them

Problem on Euler's Phi function

Working with phi function with larger numbers?

$\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k

Minimal $x$ for which $\phi(k) > n$ for all $k > x$

Updates on Lehmer's Totient Problem

Solving $\phi (n) < (n-1) \cdot \frac{15499}{94744} $

Solutions of $\phi(x)=n$ for a given n.

One problem with Euler's function

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