Question

Show that $2 ^{n(n+1)} \mid 32 · φ(2^{2^n} − 1) $

score 108 · Answer 1 · 2021-06-13 10:48:12

108

Views

Show that $2 ^{n(n+1)} \mid 32 · φ(2^{2^n} − 1) $

Published on 13 Jun 2021 - 10:48

score 40 · Answer 2 · 2021-06-23 17:45:00

40

Views

Bound number of cyclic sequences of length 2^n in alphabet {1,2}

Published on 23 Jun 2021 - 17:45

score 134 · Answer 3 · 2021-06-28 01:15:08

134

Views

Euler's Phi function congruence Proof

Published on 28 Jun 2021 - 1:15

score 98 · Answer 4 · 2026-03-27 14:39:49

98

Views

Improving $\dfrac{120}{217\zeta(3)} < \dfrac{\varphi(m)}{m}$ to $\dfrac{1}{2} < \dfrac{\varphi(m)}{m}$, where $p^k m^2$ is an odd perfect number

Published on 27 Mar 2026 - 14:39

score 292 · Answer 5 · 2021-06-30 06:38:36

292

Views

Is there any unique value for Euler Phi Function $\phi(n)$?

Published on 30 Jun 2021 - 6:38

score 161 · Answer 6 · 2021-07-12 20:19:40

161

Views

Infinitely many primes with $2$ and $3$ generating the same set of residues

Published on 12 Jul 2021 - 20:19

score 365 · Answer 7 · 2021-07-15 04:01:12

365

Views

Does the following proposition hold in number theory

Published on 15 Jul 2021 - 4:01

score 71 · Answer 8 · 2026-03-27 16:17:30

71

Views

On the equation $\frac{1}{q}=1-\frac{\varphi(N)/N}{\varphi(n)/n}$, where $N=q^k n^2$ is an odd perfect number with special prime $q$

Published on 27 Mar 2026 - 16:17

score 262 · Answer 9 · 2021-07-20 15:35:16

262

Views

Relation of totient, cycle length of multiplication and divisors

Published on 20 Jul 2021 - 15:35

score 81 · Answer 10 · 2021-07-26 12:12:20

81

Views

What percentage of binary digits in $\frac{a}{b}$ are ones?

Published on 26 Jul 2021 - 12:12

score 150 · Answer 11 · 2021-07-26 13:45:29

150

Views

Is there some function of $n$ that is a multiply of $\phi(n^2)$?

Published on 26 Jul 2021 - 13:45

score 226 · Answer 12 · 2021-08-05 21:24:28

226

Views

What is the proof that for an integer $x$, $\phi(x^2) = x \phi(x)$, where $\phi$ is Euler's totient function?

Published on 05 Aug 2021 - 21:24

score 179 · Answer 13 · 2021-08-09 18:58:50

179

Views

relatively prime solutions of $\phi(x)+\phi(y)=\phi(x+y)$

Published on 09 Aug 2021 - 18:58

score 116 · Answer 14 · 2026-03-29 03:36:18

116

Views

We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

Published on 29 Mar 2026 - 3:36

score 113 · Answer 15 · 2021-09-03 03:36:47

113

Views

If $(h,k) = 1$, then $h^{\phi(k)}\equiv 1(\textrm{mod}\ k)$?

Published on 03 Sep 2021 - 3:36

List Question

Show that $2 ^{n(n+1)} \mid 32 · φ(2^{2^n} − 1) $

Bound number of cyclic sequences of length 2^n in alphabet {1,2}

Euler's Phi function congruence Proof

Improving $\dfrac{120}{217\zeta(3)} < \dfrac{\varphi(m)}{m}$ to $\dfrac{1}{2} < \dfrac{\varphi(m)}{m}$, where $p^k m^2$ is an odd perfect number

Is there any unique value for Euler Phi Function $\phi(n)$?

Infinitely many primes with $2$ and $3$ generating the same set of residues

Does the following proposition hold in number theory

On the equation $\frac{1}{q}=1-\frac{\varphi(N)/N}{\varphi(n)/n}$, where $N=q^k n^2$ is an odd perfect number with special prime $q$

Relation of totient, cycle length of multiplication and divisors

What percentage of binary digits in $\frac{a}{b}$ are ones?

Is there some function of $n$ that is a multiply of $\phi(n^2)$?

What is the proof that for an integer $x$, $\phi(x^2) = x \phi(x)$, where $\phi$ is Euler's totient function?

relatively prime solutions of $\phi(x)+\phi(y)=\phi(x+y)$

We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

If $(h,k) = 1$, then $h^{\phi(k)}\equiv 1(\textrm{mod}\ k)$?

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