List questions from divisibility

Published on 27 Feb 2019 - 23:33

111

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Proving $3\mid p^3 \implies 3\mid p$

Published on 01 Mar 2019 - 11:46

54

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Can $p(x)\in \mathbb{F}_{3}(x)$ with $p(x)=\frac{x²+x+1}{x+1}$ be expressed as a polynomial? Is it not possible for any of the given fields?

Published on 25 Mar 2026 - 23:13

61

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Is this proof valid? $P|a^k \implies P|a$

Published on 01 Mar 2019 - 17:41

187

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Sum of squared arctangents

Published on 02 Mar 2019 - 1:16

270

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Show that if $n$ and $k$ are positive integers, then $\lceil \frac{n}{k} \rceil = \lfloor \frac{n-1}{k} \rfloor + 1$

Published on 03 Mar 2019 - 22:02

137

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number of solutions of $x^2=x$ divides the number of invertible elements in a ring

Published on 05 Mar 2019 - 21:09

61

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Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

Published on 07 Mar 2019 - 6:30

30

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Checking Proof for the following Divisibility

Published on 07 Mar 2019 - 7:39

293

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Show that $a^n-b^n$ has a prime factor which does not divide $a-b$ for all $n>1$ .

Published on 07 Mar 2019 - 19:08

38

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Base $b$ such that as many $x_b$ divide $x$ in set $\mathcal{Q}$

Published on 08 Mar 2019 - 2:13

701

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Finding integer solution to a quadratic equation in two unknowns

Published on 08 Mar 2019 - 16:25

227

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Dividers of a number

Published on 08 Mar 2019 - 17:02

585

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Prove or disprove: if $10$ divides $n^{4}$, then $10$ divides $n$

Published on 09 Mar 2019 - 1:27

114

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How to divide by decimal quickly?

Published on 11 Mar 2019 - 8:49

List Question

Unit-monic $f\mid g$ in $R[x]$ if $f\mid g$ in $S[x]$ for rings $S\supset R$

Proving $3\mid p^3 \implies 3\mid p$

Can $p(x)\in \mathbb{F}_{3}(x)$ with $p(x)=\frac{x²+x+1}{x+1}$ be expressed as a polynomial? Is it not possible for any of the given fields?

Is this proof valid? $P|a^k \implies P|a$

Sum of squared arctangents

Show that if $n$ and $k$ are positive integers, then $\lceil \frac{n}{k} \rceil = \lfloor \frac{n-1}{k} \rfloor + 1$

number of solutions of $x^2=x$ divides the number of invertible elements in a ring

Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

Checking Proof for the following Divisibility

Show that $a^n-b^n$ has a prime factor which does not divide $a-b$ for all $n>1$ .

Base $b$ such that as many $x_b$ divide $x$ in set $\mathcal{Q}$

Finding integer solution to a quadratic equation in two unknowns

Dividers of a number

Prove or disprove: if $10$ divides $n^{4}$, then $10$ divides $n$

How to divide by decimal quickly?

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