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Proving that Euler's Totient Function is multiplicative by Abstract Algebra

score 1.3k · Answer 1 · 2018-01-08 20:15:32

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Proving that Euler's Totient Function is multiplicative by Abstract Algebra

Published on 08 Jan 2018 - 20:15

score 22 · Answer 2 · 2018-01-09 11:30:05

22

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Prove: Number of (not necessarily primes) not fulfilling Fermats little theorem exceed $\frac{1}{2}\varphi(n)$

Published on 09 Jan 2018 - 11:30

score 1.1k · Answer 3 · 2018-01-11 02:13:02

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Finding all $n$ for which $\phi(n)$ is power of $2$

Published on 11 Jan 2018 - 2:13

score 133 · Answer 4 · 2018-01-11 22:58:20

133

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Calculating an euler phi of a number with a variable power

Published on 11 Jan 2018 - 22:58

score 253 · Answer 5 · 2010-10-14 18:07:34

253

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Limit involving the totient function and combination

Published on 14 Oct 2010 - 18:07

score 464 · Answer 6 · 2026-03-25 22:26:43

464

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Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$

Published on 25 Mar 2026 - 22:26

score 4.5k · Answer 7 · 2010-10-27 05:11:37

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Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$

Published on 27 Oct 2010 - 5:11

score 1.1k · Answer 8 · 2026-03-30 17:03:22

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Proving $ \frac{\sigma(n)}{n} < \frac{n}{\varphi(n)} < \frac{\pi^{2}}{6} \frac{\sigma(n)}{n}$

Published on 30 Mar 2026 - 17:03

score 5.1k · Answer 9 · 2010-12-12 21:00:57

5.1k

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Proof of the Euler Generalisation of Fermat's Little Theorem using modular arithmetic

Published on 12 Dec 2010 - 21:00

score 1.1k · Answer 10 · 2011-01-31 21:58:05

1.1k

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What is the smallest value of $n$ for which $\phi(n) \ne \phi(k)$ for any $k<n,$ where $n=4m$?

Published on 31 Jan 2011 - 21:58

score 808 · Answer 11 · 2011-03-31 20:23:34

808

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A cyclic group $C_n$ of order $n$ has $\phi(d)$ elements of order $d$ for each divisor $d$ of $n$

Published on 31 Mar 2011 - 20:23

score 2.6k · Answer 12 · 2011-04-07 10:38:32

2.6k

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Euler's phi function and distinct primes

Published on 07 Apr 2011 - 10:38

score 845 · Answer 13 · 2011-05-09 19:25:41

845

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How to derive an identity between summations of totient and Möbius functions

Published on 09 May 2011 - 19:25

score 337 · Answer 14 · 2011-06-03 02:09:01

337

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Deciding whether a given number is a totient or nontotient

Published on 03 Jun 2011 - 2:09

score 3.4k · Answer 15 · 2011-06-03 13:59:14

3.4k

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All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$

Published on 03 Jun 2011 - 13:59

List Question

Proving that Euler's Totient Function is multiplicative by Abstract Algebra

Prove: Number of (not necessarily primes) not fulfilling Fermats little theorem exceed $\frac{1}{2}\varphi(n)$

Finding all $n$ for which $\phi(n)$ is power of $2$

Calculating an euler phi of a number with a variable power

Limit involving the totient function and combination

Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$

Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$

Proving $ \frac{\sigma(n)}{n} < \frac{n}{\varphi(n)} < \frac{\pi^{2}}{6} \frac{\sigma(n)}{n}$

Proof of the Euler Generalisation of Fermat's Little Theorem using modular arithmetic

What is the smallest value of $n$ for which $\phi(n) \ne \phi(k)$ for any $k<n,$ where $n=4m$?

A cyclic group $C_n$ of order $n$ has $\phi(d)$ elements of order $d$ for each divisor $d$ of $n$

Euler's phi function and distinct primes

How to derive an identity between summations of totient and Möbius functions

Deciding whether a given number is a totient or nontotient

All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$

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