Question

Show that, for any two integers $a$ and $b$, at least one of the expressions $a^3, b^3, a^3+b^3$ or $a^3-b^3$ will be divisible by $7$.

score 445 · Answer 1 · 2017-08-26 06:51:35

445

Views

Show that, for any two integers $a$ and $b$, at least one of the expressions $a^3, b^3, a^3+b^3$ or $a^3-b^3$ will be divisible by $7$.

Published on 26 Aug 2017 - 6:51

score 97 · Answer 2 · 2017-08-26 15:43:58

97

Views

Euler's theorem and $Z_p^*$

Published on 26 Aug 2017 - 15:43

score 95 · Answer 3 · 2017-09-07 15:30:37

95

Views

What are the non-totient numbers from 300-500?

Published on 07 Sep 2017 - 15:30

score 111 · Answer 4 · 2017-09-11 09:12:16

111

Views

Are there infinitely many even integers $n$ such that $1+4\varphi(n)$ is a perfect square?

Published on 11 Sep 2017 - 9:12

score 187 · Answer 5 · 2026-03-30 13:39:06

187

Views

Are there infinitely many different primes of the form $\sigma(n^2)-\varphi(n)\sigma(n)$?

Published on 30 Mar 2026 - 13:39

score 890 · Answer 6 · 2026-03-26 08:04:41

890

Views

Solving $\tau(n)+\phi(n)=n$ for $n\in\mathbb{N})_{\ge 1}$.

Published on 26 Mar 2026 - 8:04

score 512 · Answer 7 · 2017-10-06 14:35:58

512

Views

finding remainder by using fermat's little theorem or euler's totient

Published on 06 Oct 2017 - 14:35

score 113 · Answer 8 · 2026-03-30 13:37:05

113

Views

Why is this sequence not in the Online Encyclopedia of Integer Sequences?

Published on 30 Mar 2026 - 13:37

score 1.2k · Answer 9 · 2017-10-08 06:29:15

1.2k

Views

Does $\phi(n^k) = {n^{k-1}}\phi(n)$ always hold?

Published on 08 Oct 2017 - 6:29

score 175 · Answer 10 · 2017-10-18 16:34:26

175

Views

Comparing $\phi(\phi(n))$ and the number of elements in $(\mathbb{Z}/\phi(n)\mathbb{Z})^{\times}$ of order $\le \log(n)$

Published on 18 Oct 2017 - 16:34

score 393 · Answer 11 · 2017-10-19 23:04:15

393

Views

If $n$ is an odd positive integer, then $2^{n!} − 1$ is divisible by $n$

Published on 19 Oct 2017 - 23:04

score 100 · Answer 12 · 2017-10-20 20:15:46

100

Views

On the number of applications of totient to reach 1

Published on 20 Oct 2017 - 20:15

score 413 · Answer 13 · 2017-10-24 22:44:30

413

Views

Determining when $\phi(m) + \phi(n) = \phi(mn)$.

Published on 24 Oct 2017 - 22:44

score 112 · Answer 14 · 2026-03-30 01:30:03

112

Views

Proving $\mathbb{Z}/m\mathbb{Z}\ltimes \mathbb{Z}/n\mathbb{Z}$ abelian if and only if $m$ and $\varphi(n)$ are co-prime

Published on 30 Mar 2026 - 1:30

score 348 · Answer 15 · 2026-03-29 15:51:50

348

Views

Combinatorical method proving Euler's theorem

Published on 29 Mar 2026 - 15:51

List Question

Show that, for any two integers $a$ and $b$, at least one of the expressions $a^3, b^3, a^3+b^3$ or $a^3-b^3$ will be divisible by $7$.

Euler's theorem and $Z_p^*$

What are the non-totient numbers from 300-500?

Are there infinitely many even integers $n$ such that $1+4\varphi(n)$ is a perfect square?

Are there infinitely many different primes of the form $\sigma(n^2)-\varphi(n)\sigma(n)$?

Solving $\tau(n)+\phi(n)=n$ for $n\in\mathbb{N})_{\ge 1}$.

finding remainder by using fermat's little theorem or euler's totient

Why is this sequence not in the Online Encyclopedia of Integer Sequences?

Does $\phi(n^k) = {n^{k-1}}\phi(n)$ always hold?

Comparing $\phi(\phi(n))$ and the number of elements in $(\mathbb{Z}/\phi(n)\mathbb{Z})^{\times}$ of order $\le \log(n)$

If $n$ is an odd positive integer, then $2^{n!} − 1$ is divisible by $n$

On the number of applications of totient to reach 1

Determining when $\phi(m) + \phi(n) = \phi(mn)$.

Proving $\mathbb{Z}/m\mathbb{Z}\ltimes \mathbb{Z}/n\mathbb{Z}$ abelian if and only if $m$ and $\varphi(n)$ are co-prime

Combinatorical method proving Euler's theorem

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