List questions from totient-function

Published on 27 Mar 2026 - 12:27

148

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Does Euler's $\phi$ function have the same value in arbitrarily large subsets of $\mathbb{N}$?

Published on 09 Jul 2015 - 22:39

80

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Is the relationship between these two sequences, identical but for signs, trivial?

Published on 26 Mar 2026 - 19:18

272

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Is the set $\phi(\mathbb{N})$ syndetic?

Published on 12 Jul 2015 - 10:37

811

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Application of Euler's theorem apart from finding last digits of huge numbers

Published on 13 Jul 2015 - 7:49

6.2k

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Prove that $\sum_{d|n}\phi(d)=n$ where $\phi$ is the Euler's phi function, $n,c\in\mathbb{N}$

Published on 25 Jul 2015 - 14:48

2k

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Deriving Euler's theorem from Fermat's little theorem

Published on 02 Aug 2015 - 22:51

144

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If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$

Published on 25 Mar 2026 - 19:51

446

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Prove that Euler phi function is multiplicative by a given theorem

Published on 14 Aug 2015 - 4:10

585

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

Published on 27 Mar 2026 - 12:27

310

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$\liminf_{n\to\infty} \frac{\varphi(n)}{n} = 1$, not $0$

Published on 18 Aug 2015 - 4:06

680

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Euler phi function and powers of two

Published on 18 Aug 2015 - 22:38

347

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What is $\varphi(0)$?

Published on 26 Mar 2026 - 11:16

2.1k

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$2017^{2016^{2015}} \mod 1000$

Published on 23 Aug 2015 - 11:28

204

Views

Lehmer's totient problem generalization (adding a constant )

Published on 01 Sep 2015 - 13:57

List Question

Is the Euler function $\phi$ constant in arbitrarily large intervals?

Does Euler's $\phi$ function have the same value in arbitrarily large subsets of $\mathbb{N}$?

Is the relationship between these two sequences, identical but for signs, trivial?

Is the set $\phi(\mathbb{N})$ syndetic?

Application of Euler's theorem apart from finding last digits of huge numbers

Prove that $\sum_{d|n}\phi(d)=n$ where $\phi$ is the Euler's phi function, $n,c\in\mathbb{N}$

Deriving Euler's theorem from Fermat's little theorem

If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$

Prove that Euler phi function is multiplicative by a given theorem

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

$\liminf_{n\to\infty} \frac{\varphi(n)}{n} = 1$, not $0$

Euler phi function and powers of two

What is $\varphi(0)$?

$2017^{2016^{2015}} \mod 1000$

Lehmer's totient problem generalization (adding a constant )

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