List questions from totient-function

Published on 13 Jan 2020 - 10:43

123

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Proof $\varphi(n) = n \prod_{k=1}^{z}(1-\frac{1}{p_{k}})$

Published on 16 Jan 2020 - 0:56

100

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Solution to the cototient function equation

Published on 18 Jan 2020 - 18:48

2.6k

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Proof about the Euler's totient function: $\phi(\phi(p^k)) = p^{k-2}\phi((p-1)^2)$

Published on 21 Jan 2020 - 6:41

251

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Prove that $J_r(n) = n^r\prod_{p|n}\left(1− \frac{1}{p^r}\right)$.

Published on 26 Mar 2026 - 1:04

167

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Methods for counting the number of bracelets for a 2-coloring.

Published on 25 Mar 2026 - 17:37

40

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About order of $q \pmod {p^n}.$

Published on 07 Feb 2020 - 18:43

388

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Intro Number Theory—show gcd$(\phi(m), \phi(n)) > 1$ unless either $m$ or $n$ is $1$ or $2$

Published on 25 Mar 2026 - 23:16

190

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Show that $\sum_{d \mid n} (-1)^{\frac{n}{d}} \varphi(d) = 0$ for $n$ even.

Published on 11 Feb 2020 - 23:52

108

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repeating decimals and carmichael function

Published on 25 Mar 2026 - 21:30

92

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Show that $a^{2001} \equiv a \pmod {1000}$

Published on 18 Feb 2020 - 11:12

122

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Find all the primes s.t.: $\phi\left(q^3\right)-2\phi\left(q^2\right)=q+3$

Published on 18 Feb 2020 - 14:47

45

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Why is it that for a,b∈N $φ(3^a2^b) | n$?

Published on 23 Feb 2020 - 20:40

754

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Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Published on 23 Feb 2020 - 23:38

88

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Prove that for every even positive integer $n$, $n^2 − 1$ divides $2^{n!} − 1$.

Published on 24 Feb 2020 - 0:33

List Question

Lowest Power for Euler Totient Function

Proof $\varphi(n) = n \prod_{k=1}^{z}(1-\frac{1}{p_{k}})$

Solution to the cototient function equation

Proof about the Euler's totient function: $\phi(\phi(p^k)) = p^{k-2}\phi((p-1)^2)$

Prove that $J_r(n) = n^r\prod_{p|n}\left(1− \frac{1}{p^r}\right)$.

Methods for counting the number of bracelets for a 2-coloring.

About order of $q \pmod {p^n}.$

Intro Number Theory—show gcd$(\phi(m), \phi(n)) > 1$ unless either $m$ or $n$ is $1$ or $2$

Show that $\sum_{d \mid n} (-1)^{\frac{n}{d}} \varphi(d) = 0$ for $n$ even.

repeating decimals and carmichael function

Show that $a^{2001} \equiv a \pmod {1000}$

Find all the primes s.t.: $\phi\left(q^3\right)-2\phi\left(q^2\right)=q+3$

Why is it that for a,b∈N $φ(3^a2^b) | n$?

Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Prove that for every even positive integer $n$, $n^2 − 1$ divides $2^{n!} − 1$.

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