Question

Is there a polynomial $P(n)$ such that $nP(n) = \varphi(n)$, or also $\varphi(n)P(n)$ is a square number?

score 85 · Answer 1 · 2021-03-30 08:45:26

85

Views

Is there a polynomial $P(n)$ such that $nP(n) = \varphi(n)$, or also $\varphi(n)P(n)$ is a square number?

Published on 30 Mar 2021 - 8:45

score 73 · Answer 2 · 2021-03-30 17:41:22

73

Views

$\sigma_0(n)=\varphi(n)$

Published on 30 Mar 2021 - 17:41

score 48 · Answer 3 · 2021-04-02 12:08:57

48

Views

Is there a calculable alternative for totient function when the base is $2$?

Published on 02 Apr 2021 - 12:08

score 120 · Answer 4 · 2021-04-04 06:03:49

120

Views

Composition of Euler's $\phi$ function

Published on 04 Apr 2021 - 6:03

score 75 · Answer 5 · 2021-04-05 10:56:51

75

Views

Using Euler totient function to show density of primes is 0.

Published on 05 Apr 2021 - 10:56

score 234 · Answer 6 · 2026-03-27 05:42:34

234

Views

When is $\lambda (n)$ = $\phi (n)$?

Published on 27 Mar 2026 - 5:42

score 50 · Answer 7 · 2021-04-08 18:28:45

50

Views

find m if $m = p_1^2p_2^2$ and $\varphi(m) = 11424$

Published on 08 Apr 2021 - 18:28

score 64 · Answer 8 · 2021-04-12 06:11:30

64

Views

Why is $\sum_{d\mid n}\varphi(n/d)=\sum_{d\mid n}\varphi(d)$?

Published on 12 Apr 2021 - 6:11

score 277 · Answer 9 · 2021-04-12 20:14:57

277

Views

$1 = \phi(\phi(\cdots\phi(n)\cdots))$, where Euler's totient is applied $k$ times, then $n\leq 3^k$

Published on 12 Apr 2021 - 20:14

score 41 · Answer 10 · 2021-04-24 16:49:11

41

Views

Getting wrong results for multiple power mod 11

Published on 24 Apr 2021 - 16:49

score 518 · Answer 11 · 2021-05-13 05:27:01

518

Views

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

Published on 13 May 2021 - 5:27

score 185 · Answer 12 · 2021-05-14 15:46:18

185

Views

If every Prime-Divisor of m is a prime-Divisor of n ist, then φ(mn) = mφ(n)

Published on 14 May 2021 - 15:46

score 103 · Answer 13 · 2026-02-23 09:32:39

103

Views

For integers $m>2, n>1, c> 0$, with $2^m - 3^n=c$, does it follow for integers $x>0,y>0$ that $2^{m+x} - 3^{n+y} \ne c$

Published on 23 Feb 2026 - 9:32

score 1.2k · Answer 14 · 2026-03-30 08:31:17

1.2k

Views

which Numbers can have primitive roots?

Published on 30 Mar 2026 - 8:31

score 195 · Answer 15 · 2026-03-26 13:01:52

195

Views

The function $ g(n)=\sum_{\substack {1\lt k\leq n \\ \gcd(k,n)=1}}d(k-1)$

Published on 26 Mar 2026 - 13:01

List Question

Is there a polynomial $P(n)$ such that $nP(n) = \varphi(n)$, or also $\varphi(n)P(n)$ is a square number?

$\sigma_0(n)=\varphi(n)$

Is there a calculable alternative for totient function when the base is $2$?

Composition of Euler's $\phi$ function

Using Euler totient function to show density of primes is 0.

When is $\lambda (n)$ = $\phi (n)$?

find m if $m = p_1^2p_2^2$ and $\varphi(m) = 11424$

Why is $\sum_{d\mid n}\varphi(n/d)=\sum_{d\mid n}\varphi(d)$?

$1 = \phi(\phi(\cdots\phi(n)\cdots))$, where Euler's totient is applied $k$ times, then $n\leq 3^k$

Getting wrong results for multiple power mod 11

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

If every Prime-Divisor of m is a prime-Divisor of n ist, then φ(mn) = mφ(n)

For integers $m>2, n>1, c> 0$, with $2^m - 3^n=c$, does it follow for integers $x>0,y>0$ that $2^{m+x} - 3^{n+y} \ne c$

which Numbers can have primitive roots?

The function $ g(n)=\sum_{\substack {1\lt k\leq n \\ \gcd(k,n)=1}}d(k-1)$

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