List questions from divisibility

Published on 01 Aug 2016 - 13:20

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Proving the fraction $\frac{n^3 + 2n}{n^4 + 3n^2 + 1}$ is irreducible for $n \in \mathbb{N}$

Published on 29 Mar 2026 - 22:33

73

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When does $\sum_{j=1}^n j$ divide $\prod_{j=1}^n j$?

Published on 02 Aug 2016 - 13:11

94

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On the proof of $a^n \mid b^n \implies a \mid b$

Published on 03 Aug 2016 - 14:09

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If $n$ is an integer then $4$ does not divide $n^2 - 3$

Published on 03 Aug 2016 - 19:55

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Word problem "what number am I?"

Published on 27 Mar 2026 - 15:11

35

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find the number of pairs $(a,b)$ where $a,b,n\in\mathbb N$ and $1\le a<b\le n$ and $b|(a^2-1)$ and $a|(b^2-1)$

Published on 29 Mar 2026 - 23:46

1.5k

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Every prime number divide some sum of the first $k$ primes.

Published on 27 Mar 2026 - 14:02

94

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how many divisor of 10010000 which are multiple of $52$?

Published on 05 Aug 2016 - 5:22

1.3k

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Shorter proof of irrationality of $\sqrt{2}$?

Published on 25 Mar 2026 - 22:04

130

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Find all pairs $(a,b)$ of positive integers, such that $(a+1)(b+1)$ is divisible by $ab$.

Published on 08 Aug 2016 - 8:41

1k

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Prime dividing sum of divisors

Published on 25 Mar 2026 - 19:04

61

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Minimum number of divisibility tests required in order to identify a number between $1$ and $n$

Published on 09 Aug 2016 - 7:27

230

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Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

Published on 09 Aug 2016 - 10:11

41

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How we can find number $b$ which is divisor of two divison

Published on 09 Aug 2016 - 10:17

List Question

Use induction to prove that $6$ divides $n^3 - n$.

Proving the fraction $\frac{n^3 + 2n}{n^4 + 3n^2 + 1}$ is irreducible for $n \in \mathbb{N}$

When does $\sum_{j=1}^n j$ divide $\prod_{j=1}^n j$?

On the proof of $a^n \mid b^n \implies a \mid b$

If $n$ is an integer then $4$ does not divide $n^2 - 3$

Word problem "what number am I?"

find the number of pairs $(a,b)$ where $a,b,n\in\mathbb N$ and $1\le a<b\le n$ and $b|(a^2-1)$ and $a|(b^2-1)$

Every prime number divide some sum of the first $k$ primes.

how many divisor of 10010000 which are multiple of $52$?

Shorter proof of irrationality of $\sqrt{2}$?

Find all pairs $(a,b)$ of positive integers, such that $(a+1)(b+1)$ is divisible by $ab$.

Prime dividing sum of divisors

Minimum number of divisibility tests required in order to identify a number between $1$ and $n$

Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

How we can find number $b$ which is divisor of two divison

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