List questions from divisibility

Published on 26 Mar 2026 - 5:55

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How can I find integers which satisfy $\frac{150+n}{15+n}=m$?

Published on 27 Mar 2026 - 3:43

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Simpler ways to show that $n^2$ divides a polynomial?

Published on 26 Mar 2026 - 22:17

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Determine the number of positive integers $a$ such that $a\mid 9!$ and gcd $(a, 3600)=180$.

Published on 26 Mar 2026 - 4:53

106

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Divisibility by 11 proof

Published on 13 Dec 2018 - 0:32

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Find all positive integer $m$ such $2^{m}+1\mid5^m-1$

Published on 13 Dec 2018 - 8:13

108

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What is the general solution of $x+y+z \mid xyz$?

Published on 13 Dec 2018 - 9:42

145

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Sum of freely chosen subset of $n$-tuple is divisible by $n$.

Published on 13 Dec 2018 - 12:11

408

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Divisors of a cyclotomic polynomial

Published on 25 Mar 2026 - 20:41

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Divisibilty vs. division, for negative divisors

Published on 15 Dec 2018 - 1:26

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Let $g(k)$ be the greatest odd divisor of $k$ show that $ 0< \sum_{k=1}^n \frac {g(k)}{k} - \frac {2n}{3} \lt \frac 23$

Published on 15 Dec 2018 - 5:19

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Let $x \in \mathbb{N}$ and let $p$ be a prime divisor of $x^4+x^3+x^2+x+1$, prove that $p = 5$ or $p \equiv 1 \mod{5}$

Published on 16 Dec 2018 - 13:57

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Disprove that if $n$ is an odd positive integer greater than $1$ then $2^n-1$ is prime.

Published on 16 Dec 2018 - 19:28

545

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If $xy$ divides $x^2 + y^2$ show that $x=\pm y$

Published on 26 Mar 2026 - 9:42

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$17 | 29x + 18y \implies 17 | 23x + 9y$

Published on 19 Dec 2018 - 12:13

List Question

Number of divisors of $10!$

How can I find integers which satisfy $\frac{150+n}{15+n}=m$?

Simpler ways to show that $n^2$ divides a polynomial?

Determine the number of positive integers $a$ such that $a\mid 9!$ and gcd $(a, 3600)=180$.

Divisibility by 11 proof

Find all positive integer $m$ such $2^{m}+1\mid5^m-1$

What is the general solution of $x+y+z \mid xyz$?

Sum of freely chosen subset of $n$-tuple is divisible by $n$.

Divisors of a cyclotomic polynomial

Divisibilty vs. division, for negative divisors

Let $g(k)$ be the greatest odd divisor of $k$ show that $ 0< \sum_{k=1}^n \frac {g(k)}{k} - \frac {2n}{3} \lt \frac 23$

Let $x \in \mathbb{N}$ and let $p$ be a prime divisor of $x^4+x^3+x^2+x+1$, prove that $p = 5$ or $p \equiv 1 \mod{5}$

Disprove that if $n$ is an odd positive integer greater than $1$ then $2^n-1$ is prime.

If $xy$ divides $x^2 + y^2$ show that $x=\pm y$

$17 | 29x + 18y \implies 17 | 23x + 9y$

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