Question

When is $ 2^n-1=0\bmod (n^2-1) $?

score 47 · Answer 1 · 2020-04-24 02:08:53

47

Views

When is $ 2^n-1=0\bmod (n^2-1) $?

Published on 24 Apr 2020 - 2:08

score 53 · Answer 2 · 2020-04-24 12:31:05

53

Views

Proving that $2^{2018}-2^{2016}+2^{2013}$ is divisible by $5$.

Published on 24 Apr 2020 - 12:31

score 342 · Answer 3 · 2026-02-23 04:59:07

342

Views

Can a composite number $3\cdot 2^n + 1$ divide a Fermat number $2^{2^m}+1$?

Published on 23 Feb 2026 - 4:59

score 64 · Answer 4 · 2026-03-27 15:20:03

64

Views

If $(x_n)_{n\in\mathbb N}$ is subadditive, show that $x_n\le\left\lfloor\frac nk\right\rfloor x_k+x_{n-k\left\lfloor\frac nk\right\rfloor}$

Published on 27 Mar 2026 - 15:20

score 304 · Answer 5 · 2026-03-29 07:45:57

304

Views

Problem from the 1998 Hungarian Math Olympiad

Published on 29 Mar 2026 - 7:45

score 30 · Answer 6 · 2020-04-27 20:43:18

30

Views

Consequences in number theory if we have ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k>1$?

Published on 27 Apr 2020 - 20:43

score 206 · Answer 7 · 2026-03-25 17:38:56

206

Views

'Contain is to divide' doesn't imply Dedekind Domain

Published on 25 Mar 2026 - 17:38

score 80 · Answer 8 · 2020-04-30 19:58:14

80

Views

There exist $a,b$ integers such that $a³+b³=311$?

Published on 30 Apr 2020 - 19:58

score 92 · Answer 9 · 2026-03-29 07:45:57

92

Views

Algebra question on transformation of an n-tuple to $a = (a_1, \dots , a_n)$ to $(1, 0, \dots ,0)$

Published on 29 Mar 2026 - 7:45

score 53 · Answer 10 · 2020-05-02 01:17:23

53

Views

Necessity of coprimeness in Carmichael numbers

Published on 02 May 2020 - 1:17

score 54 · Answer 11 · 2020-05-02 06:02:36

54

Views

all positive integers satisfying the following series

Published on 02 May 2020 - 6:02

score 585 · Answer 12 · 2020-05-02 11:27:44

585

Views

Finding smallest possible integer to satisfy a perfect cube

Published on 02 May 2020 - 11:27

score 49 · Answer 13 · 2026-04-02 02:02:29

49

Views

$a,b\in\mathbb{N}$. How many points with integers coordinates exist between $(a,0)$ and $(0,b)$?

Published on 02 Apr 2026 - 2:02

score 183 · Answer 14 · 2026-03-27 10:31:34

183

Views

Help with this problem about a constructed number, that is from an arbitary n numbers, and that is divisible by a prime

Published on 27 Mar 2026 - 10:31

score 125 · Answer 15 · 2020-05-03 15:02:09

125

Views

Proving that when $n$ is not a power of 2, $\exists k, 0 < k < n$ such that $\binom{n}{k}$ is odd

Published on 03 May 2020 - 15:02

List Question

When is $ 2^n-1=0\bmod (n^2-1) $?

Proving that $2^{2018}-2^{2016}+2^{2013}$ is divisible by $5$.

Can a composite number $3\cdot 2^n + 1$ divide a Fermat number $2^{2^m}+1$?

If $(x_n)_{n\in\mathbb N}$ is subadditive, show that $x_n\le\left\lfloor\frac nk\right\rfloor x_k+x_{n-k\left\lfloor\frac nk\right\rfloor}$

Problem from the 1998 Hungarian Math Olympiad

Consequences in number theory if we have ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k>1$?

'Contain is to divide' doesn't imply Dedekind Domain

There exist $a,b$ integers such that $a³+b³=311$?

Algebra question on transformation of an n-tuple to $a = (a_1, \dots , a_n)$ to $(1, 0, \dots ,0)$

Necessity of coprimeness in Carmichael numbers

all positive integers satisfying the following series

Finding smallest possible integer to satisfy a perfect cube

$a,b\in\mathbb{N}$. How many points with integers coordinates exist between $(a,0)$ and $(0,b)$?

Help with this problem about a constructed number, that is from an arbitary n numbers, and that is divisible by a prime

Proving that when $n$ is not a power of 2, $\exists k, 0 < k < n$ such that $\binom{n}{k}$ is odd

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