Question

Calculate Euler's totient function for perfect squares

score 1.7k · Answer 1 · 2018-09-11 06:03:57

1.7k

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Calculate Euler's totient function for perfect squares

Published on 11 Sep 2018 - 6:03

score 958 · Answer 2 · 2018-09-14 01:00:09

958

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Given $\varphi (n)$ and $n$ for large values, can we know prime factors of $n$

Published on 14 Sep 2018 - 1:00

score 216 · Answer 3 · 2018-09-17 07:23:59

216

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Evaluating $\sum_{n=1}^{\infty} \frac{\phi(n)}{7^n + 1}$, where $\phi(n)$ is Euler's totient function

Published on 17 Sep 2018 - 7:23

score 247 · Answer 4 · 2026-03-25 17:36:36

247

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Euler's totient function applied to higher power triples

Published on 25 Mar 2026 - 17:36

score 526 · Answer 5 · 2018-09-21 13:12:28

526

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For any $a$, can we find $b$ and $c$ such that $\phi(a^2)+\phi(b^2)=\phi(c^2)$? ($\phi$ is Euler's totient function.)

Published on 21 Sep 2018 - 13:12

score 726 · Answer 6 · 2026-03-25 12:33:08

726

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Application of Euler's totient function to find last digits

Published on 25 Mar 2026 - 12:33

score 327 · Answer 7 · 2018-10-01 17:19:37

327

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Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$

Published on 01 Oct 2018 - 17:19

score 440 · Answer 8 · 2018-10-03 20:06:30

440

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Invertible elements $\mathbb{Z} / p^2 \mathbb{Z}$

Published on 03 Oct 2018 - 20:06

score 47 · Answer 9 · 2018-10-04 02:28:22

47

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How to prove $a^{k\times \phi(n)+1} \equiv a\ (mod\ n$)?

Published on 04 Oct 2018 - 2:28

score 349 · Answer 10 · 2018-10-04 08:46:15

349

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Proof if $x$ is order $\phi(n)$ in $\mathbb{Z}/n \mathbb{Z}$ all inverses are powers of $x$.

Published on 04 Oct 2018 - 8:46

score 1k · Answer 11 · 2018-10-04 23:49:48

1k

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using euler's theorem (phi/totient function) to compute order of group elements

Published on 04 Oct 2018 - 23:49

score 2.5k · Answer 12 · 2018-10-06 16:23:47

2.5k

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Show that if $ p\mid n$ then $\phi(np)=p\phi(n)$

Published on 06 Oct 2018 - 16:23

score 130 · Answer 13 · 2018-10-08 00:43:37

130

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Prove that a finite cyclic group of order $n>2$ has an even number of distinct generators. What can you deduce about $\phi(n)$ when $n>2$?

Published on 08 Oct 2018 - 0:43

score 193 · Answer 14 · 2018-10-14 21:55:12

193

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Proving Euler-Fermat's Theorem

Published on 14 Oct 2018 - 21:55

score 3.1k · Answer 15 · 2018-10-16 05:16:38

3.1k

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Find all numbers $n$ such that $\phi (n) = 20$

Published on 16 Oct 2018 - 5:16

List Question

Calculate Euler's totient function for perfect squares

Given $\varphi (n)$ and $n$ for large values, can we know prime factors of $n$

Evaluating $\sum_{n=1}^{\infty} \frac{\phi(n)}{7^n + 1}$, where $\phi(n)$ is Euler's totient function

Euler's totient function applied to higher power triples

For any $a$, can we find $b$ and $c$ such that $\phi(a^2)+\phi(b^2)=\phi(c^2)$? ($\phi$ is Euler's totient function.)

Application of Euler's totient function to find last digits

Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$

Invertible elements $\mathbb{Z} / p^2 \mathbb{Z}$

How to prove $a^{k\times \phi(n)+1} \equiv a\ (mod\ n$)?

Proof if $x$ is order $\phi(n)$ in $\mathbb{Z}/n \mathbb{Z}$ all inverses are powers of $x$.

using euler's theorem (phi/totient function) to compute order of group elements

Show that if $ p\mid n$ then $\phi(np)=p\phi(n)$

Prove that a finite cyclic group of order $n>2$ has an even number of distinct generators. What can you deduce about $\phi(n)$ when $n>2$?

Proving Euler-Fermat's Theorem

Find all numbers $n$ such that $\phi (n) = 20$

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