Question

Dividing polynomial $f(x^3)$ by $x^2+x+1$

score 98 · Answer 1 · 2020-05-04 06:57:54

98

Views

Dividing polynomial $f(x^3)$ by $x^2+x+1$

Published on 04 May 2020 - 6:57

score 94 · Answer 2 · 2020-05-04 11:35:50

94

Views

There are two positive integers of the form $p-n^2$ such that one divides the other.

Published on 04 May 2020 - 11:35

score 53 · Answer 3 · 2020-05-04 14:55:02

53

Views

A function divisible by $p$

Published on 04 May 2020 - 14:55

score 70 · Answer 4 · 2020-05-04 16:54:31

70

Views

Find the value of the prime $p$ knowing that $p>5$ and $p│(3^{p+1} +5^{p-1} + 1)$

Published on 04 May 2020 - 16:54

score 289 · Answer 5 · 2020-05-04 19:26:03

289

Views

Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$

Published on 04 May 2020 - 19:26

score 53 · Answer 6 · 2020-05-05 10:31:51

53

Views

Solve equation with constrain on number of decimals?

Published on 05 May 2020 - 10:31

score 282 · Answer 7 · 2020-05-06 14:07:44

282

Views

Long division answer differs to calculator answer

Published on 06 May 2020 - 14:07

score 123 · Answer 8 · 2026-03-27 18:27:58

123

Views

Is it true or can it be proven that $\frac{n}{\varphi(n)} \geq \operatorname{rad}(n)$?

Published on 27 Mar 2026 - 18:27

score 164 · Answer 9 · 2026-02-23 08:28:36

164

Views

School-level problem on divisibility

Published on 23 Feb 2026 - 8:28

score 69 · Answer 10 · 2020-05-07 18:03:08

Consider $f(x) = x^5 + 2x^4 + x^3 + 2x^2 + x + 1 \in \mathbb{F}_3[x]$. Find the smallest $m\in\mathbb{N}$ such that f(x) divides $x^{3^m}-x$.

score 60 · Answer 11 · 2020-05-08 11:25:34

60

Views

I don't know if I'm correct.

Published on 08 May 2020 - 11:25

score 111 · Answer 12 · 2020-05-09 10:03:30

111

Views

Prove that for odd $n > 1$ , $3^{n} + 1$ is not divisible by $n$

Published on 09 May 2020 - 10:03

score 679 · Answer 13 · 2020-05-10 13:56:49

679

Views

When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.

Published on 10 May 2020 - 13:56

score 1.4k · Answer 14 · 2026-03-29 08:14:41

1.4k

Views

How to find k'th integer not divisible by n?

Published on 29 Mar 2026 - 8:14

score 113 · Answer 15 · 2026-04-03 06:17:42

113

Views

If $\alpha, \beta$ are the roots of the equation $x^2-(p+1)x+1=0.$ show that $\alpha^n + \beta^n$ is not divisible by $p$ $(p \ge3)$

Published on 03 Apr 2026 - 6:17

List Question

Dividing polynomial $f(x^3)$ by $x^2+x+1$

There are two positive integers of the form $p-n^2$ such that one divides the other.

A function divisible by $p$

Find the value of the prime $p$ knowing that $p>5$ and $p│(3^{p+1} +5^{p-1} + 1)$

Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$

Solve equation with constrain on number of decimals?

Long division answer differs to calculator answer

Is it true or can it be proven that $\frac{n}{\varphi(n)} \geq \operatorname{rad}(n)$?

School-level problem on divisibility

Consider $f(x) = x^5 + 2x^4 + x^3 + 2x^2 + x + 1 \in \mathbb{F}_3[x]$. Find the smallest $m\in\mathbb{N}$ such that f(x) divides $x^{3^m}-x$.

I don't know if I'm correct.

Prove that for odd $n > 1$ , $3^{n} + 1$ is not divisible by $n$

When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.

How to find k'th integer not divisible by n?

If $\alpha, \beta$ are the roots of the equation $x^2-(p+1)x+1=0.$ show that $\alpha^n + \beta^n$ is not divisible by $p$ $(p \ge3)$

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