Question

Miscellaneous conjectures about perfect numbers related to the quantity $\varphi\left(103\frac{\sigma(n)}{2}+107n\right)$

score 104 · Answer 1 · 2026-03-25 15:43:44

104

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Miscellaneous conjectures about perfect numbers related to the quantity $\varphi\left(103\frac{\sigma(n)}{2}+107n\right)$

Published on 25 Mar 2026 - 15:43

score 65 · Answer 2 · 2026-03-25 07:43:12

65

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This should be a reduced residue system rather than a complete residue system, right?

Published on 25 Mar 2026 - 7:43

score 61 · Answer 3 · 2019-07-16 09:11:10

61

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What is the significance of $(n,m)=1$ in this proof that the Euler phi function is multiplicative?

Published on 16 Jul 2019 - 9:11

score 256 · Answer 4 · 2019-07-18 12:08:31

256

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Questions on a proof to show if $\Phi(n)=\sum^n_{i=1}\phi(i)$, where $\phi$ is the Euler phi function then $\Phi(n)=\tfrac{3n^2}{\pi}+O(n\log(n))$

Published on 18 Jul 2019 - 12:08

score 408 · Answer 5 · 2019-07-19 04:29:10

408

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A Hypothesis about Euler's Totient Theorem

Published on 19 Jul 2019 - 4:29

score 291 · Answer 6 · 2019-07-24 21:55:49

291

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Euler's totient problem: Prove that the order of $2 \bmod 5^n$ is always equal to $4\cdot 5^{n-1}$

Published on 24 Jul 2019 - 21:55

score 785 · Answer 7 · 2019-07-31 17:46:42

785

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Solutions to $\varphi(\varphi(a))=\varphi(\varphi(b))$

Published on 31 Jul 2019 - 17:46

score 136 · Answer 8 · 2019-08-11 13:25:19

136

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Estimating the sum reciprocal of the Totient Function

Published on 11 Aug 2019 - 13:25

score 79 · Answer 9 · 2019-08-16 03:39:38

79

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Prove Euler totient $\phi(p^k)=p^k(1-\frac{1}{p})$ with group theory?

Published on 16 Aug 2019 - 3:39

score 304 · Answer 10 · 2019-08-22 18:26:46

304

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How does Chinese Remainder theorem help prove $\phi(ab) = \phi(a)\phi(b)$?

Published on 22 Aug 2019 - 18:26

score 223 · Answer 11 · 2019-08-23 17:19:56

223

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Criterion for $\phi(mn)=m\phi(n)$ to be true

Published on 23 Aug 2019 - 17:19

score 248 · Answer 12 · 2019-08-25 16:34:47

248

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Sum of Eulers phi function

Published on 25 Aug 2019 - 16:34

score 121 · Answer 13 · 2019-08-27 12:11:35

121

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What is the remainder of $2^{4000}$ divided by 99?

Published on 27 Aug 2019 - 12:11

score 46 · Answer 14 · 2019-08-31 17:05:34

46

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To prove $\gcd\{p^2-1: p $ is a prime $ \geq 7 \}=24$

Published on 31 Aug 2019 - 17:05

score 90 · Answer 15 · 2019-09-09 18:53:20

For each positive integer $k$, there is a positive integer $m\neq 3k$ such that $\varphi(3k)=\varphi(m)$ (with $\varphi(n)$ being Euler's totient)

List Question

Miscellaneous conjectures about perfect numbers related to the quantity $\varphi\left(103\frac{\sigma(n)}{2}+107n\right)$

This should be a reduced residue system rather than a complete residue system, right?

What is the significance of $(n,m)=1$ in this proof that the Euler phi function is multiplicative?

Questions on a proof to show if $\Phi(n)=\sum^n_{i=1}\phi(i)$, where $\phi$ is the Euler phi function then $\Phi(n)=\tfrac{3n^2}{\pi}+O(n\log(n))$

A Hypothesis about Euler's Totient Theorem

Euler's totient problem: Prove that the order of $2 \bmod 5^n$ is always equal to $4\cdot 5^{n-1}$

Solutions to $\varphi(\varphi(a))=\varphi(\varphi(b))$

Estimating the sum reciprocal of the Totient Function

Prove Euler totient $\phi(p^k)=p^k(1-\frac{1}{p})$ with group theory?

How does Chinese Remainder theorem help prove $\phi(ab) = \phi(a)\phi(b)$?

Criterion for $\phi(mn)=m\phi(n)$ to be true

Sum of Eulers phi function

What is the remainder of $2^{4000}$ divided by 99?

To prove $\gcd\{p^2-1: p $ is a prime $ \geq 7 \}=24$

For each positive integer $k$, there is a positive integer $m\neq 3k$ such that $\varphi(3k)=\varphi(m)$ (with $\varphi(n)$ being Euler's totient)

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