List questions from totient-function

Published on 09 Jul 2011 - 18:35

222

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A property of the totient function

Published on 26 Jul 2011 - 11:17

375

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How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?

Published on 27 Mar 2026 - 10:46

2.1k

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How many irreducible fractions between 0 and 1 have denominator less than $n$?

Published on 21 Aug 2011 - 3:34

7.3k

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Why does $\phi(pq)=\phi(p)\phi(q)$?

Published on 21 Sep 2011 - 23:44

1.4k

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Why is $f(x) = x\phi(x)$ injective, i.e. $x\phi(x) = y\phi(y)\Rightarrow x = y$

Published on 28 Sep 2011 - 3:40

1.6k

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Why is 2 totative of 36?

Published on 22 Oct 2011 - 20:01

662

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Proof: $\phi(n)=\sum\limits_{k=1}^{n-1} \left\lfloor\frac{1}{\operatorname{gcd}(n,k)} \right\rfloor$

Published on 28 Oct 2011 - 12:09

2k

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Finding the maximum number with a certain Euler's totient value

Published on 31 Oct 2011 - 5:40

1.2k

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Is there a methodical way to compute Euler's Phi function

Published on 06 Nov 2011 - 14:14

597

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Nice formula for $\sum\limits_{d|n}(-1)^{n/d}\Phi(d)$?

Published on 21 Nov 2011 - 16:45

2.1k

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

Published on 26 Mar 2026 - 4:14

2.1k

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How can I show $e^2 \equiv 1 \bmod 24$, given that $\gcd(e, 24) = 1$?

Published on 17 Dec 2011 - 17:06

488

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Proof that $\binom{2\phi(r)}{\phi(r)+1} \geq 2^{\phi(r)}$

Published on 30 Dec 2011 - 12:25

26k

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Using Euler's Totient Function, how do I find all values n such that $\phi(n)=12$?

Published on 23 Jan 2012 - 8:14

List Question

Proof of Euler's Theorem without abstract algebra?

A property of the totient function

How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?

How many irreducible fractions between 0 and 1 have denominator less than $n$?

Why does $\phi(pq)=\phi(p)\phi(q)$?

Why is $f(x) = x\phi(x)$ injective, i.e. $x\phi(x) = y\phi(y)\Rightarrow x = y$

Why is 2 totative of 36?

Proof: $\phi(n)=\sum\limits_{k=1}^{n-1} \left\lfloor\frac{1}{\operatorname{gcd}(n,k)} \right\rfloor$

Finding the maximum number with a certain Euler's totient value

Is there a methodical way to compute Euler's Phi function

Nice formula for $\sum\limits_{d|n}(-1)^{n/d}\Phi(d)$?

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

How can I show $e^2 \equiv 1 \bmod 24$, given that $\gcd(e, 24) = 1$?

Proof that $\binom{2\phi(r)}{\phi(r)+1} \geq 2^{\phi(r)}$

Using Euler's Totient Function, how do I find all values n such that $\phi(n)=12$?

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