List questions from divisibility

Published on 29 Mar 2026 - 20:52

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Using mathematical induction to prove a divisibility

Published on 28 Mar 2020 - 1:50

64

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Integer solutions to $(a^x - b^y)/(a - b)=c$

Published on 01 Apr 2026 - 19:23

76

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Prove that for every $n\in\mathbb{N}$, $n^2$ is divisible by 3 or has a form $3k+1$?

Published on 28 Mar 2020 - 19:43

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Proof: If a|b, then a|bc.

Published on 29 Mar 2020 - 1:36

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$a+b \mid ab$ from CMO 1996

Published on 29 Mar 2020 - 6:31

65

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Prove that $\frac{(mn)!}{(n!)^{m+1}}$ is an integer.

Published on 30 Mar 2026 - 6:10

70

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Why the sum of the digits of $9k+a$ (where $k,a\in \mathbb{N}$, and $0<a<8$) is equal to $9l+a$ (where $\mathbb{N}\ni l< k$)?

Published on 29 Mar 2026 - 20:51

259

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Find all positive integers n such that 20n+2 can divide 2003n+2002

Published on 31 Mar 2020 - 4:46

71

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Divisibility of odd numbers and its sum of divisors function - Part II

Published on 28 Mar 2026 - 10:04

29

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Can this congruence rule be generalized?

Published on 31 Mar 2020 - 22:44

257

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For a prime q and positive integers x, y, z, w , q divides yz, q divides xy and q doesn't divide yw implies that q^2 divides xz

Published on 01 Apr 2020 - 7:50

295

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Divisibility of cyclic sums

Published on 01 Apr 2020 - 9:31

192

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Find all positive integers $n$ such that $n^2 \not\mid (n - 2)!$

Published on 02 Apr 2020 - 1:17

141

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How can you prove the existence of an integer for ab congruent to 1 (mod p).

Published on 02 Apr 2020 - 5:19

List Question

For which $n\in\mathbb{N}$ is $(n+2)\mid(n^3+14)$ true?

Using mathematical induction to prove a divisibility

Integer solutions to $(a^x - b^y)/(a - b)=c$

Prove that for every $n\in\mathbb{N}$, $n^2$ is divisible by 3 or has a form $3k+1$?

Proof: If a|b, then a|bc.

$a+b \mid ab$ from CMO 1996

Prove that $\frac{(mn)!}{(n!)^{m+1}}$ is an integer.

Why the sum of the digits of $9k+a$ (where $k,a\in \mathbb{N}$, and $0<a<8$) is equal to $9l+a$ (where $\mathbb{N}\ni l< k$)?

Find all positive integers n such that 20n+2 can divide 2003n+2002

Divisibility of odd numbers and its sum of divisors function - Part II

Can this congruence rule be generalized?

For a prime q and positive integers x, y, z, w , q divides yz, q divides xy and q doesn't divide yw implies that q^2 divides xz

Divisibility of cyclic sums

Find all positive integers $n$ such that $n^2 \not\mid (n - 2)!$

How can you prove the existence of an integer for ab congruent to 1 (mod p).

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