List questions from divisibility

Published on 09 Oct 2018 - 2:38

70

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Is there a typo about the theorem of divisibility in The Theory of Numbers book by Ivan Niven; Herbert Zuckerman; Hugh Montgomery?

Published on 09 Oct 2018 - 7:25

67

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Euclide arithmetic, divisibility

Published on 09 Oct 2018 - 17:06

116

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Proving $7|13\cdot 6^{n}+8\cdot 13^{n}$ for all natural numbers.

Published on 09 Oct 2018 - 21:03

64

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Dividing $n^k+1$ by $n+1$ if and only if $k$ is odd

Published on 11 Oct 2018 - 14:01

78

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What is the remainder when $1\times 1! + 2\times 2! + 3\times 3! +\ldots+ 11\times 11! + 3$ is divided by $12!$?

Published on 25 Mar 2026 - 23:13

127

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Factor $10^6-1$ completely

Published on 26 Mar 2026 - 3:10

188

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Divisibility Proof $8^n\mid(4n)!$

Published on 25 Mar 2026 - 23:16

511

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Prove that gcd$(n^2+1, (n+1)^2+1)$ is either 1 or 5

Published on 26 Mar 2026 - 3:11

119

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"Although it is necessary for $n$ to be prime in order for $R_n$ to be prime" as logic statement

Published on 25 Mar 2026 - 3:03

6.9k

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Prove that $3\cdot 5^{2n+1} +2^{3n+1}$ is divisible by $17$ for all $n ∈ \mathbb{N}$

Published on 15 Oct 2018 - 8:33

152

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Linear Diophantine equation which doesn't divide

Published on 25 Mar 2026 - 4:36

2.3k

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Prove that $7^n+2$ is divisible by $3$ for all $n ∈ \mathbb{N}$

Published on 16 Oct 2018 - 13:47

4.9k

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How many positive divisors of 2000?

Published on 17 Oct 2018 - 12:51

2.5k

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For any primitive pythagorean triple $(a,b,c)$ either $a$ or $b$ must be a multiple of $3$

Published on 25 Mar 2026 - 19:05

List Question

Can $pk+1$ divide $(p-k)^2$?

Is there a typo about the theorem of divisibility in The Theory of Numbers book by Ivan Niven; Herbert Zuckerman; Hugh Montgomery?

Euclide arithmetic, divisibility

Proving $7|13\cdot 6^{n}+8\cdot 13^{n}$ for all natural numbers.

Dividing $n^k+1$ by $n+1$ if and only if $k$ is odd

What is the remainder when $1\times 1! + 2\times 2! + 3\times 3! +\ldots+ 11\times 11! + 3$ is divided by $12!$?

Factor $10^6-1$ completely

Divisibility Proof $8^n\mid(4n)!$

Prove that gcd$(n^2+1, (n+1)^2+1)$ is either 1 or 5

"Although it is necessary for $n$ to be prime in order for $R_n$ to be prime" as logic statement

Prove that $3\cdot 5^{2n+1} +2^{3n+1}$ is divisible by $17$ for all $n ∈ \mathbb{N}$

Linear Diophantine equation which doesn't divide

Prove that $7^n+2$ is divisible by $3$ for all $n ∈ \mathbb{N}$

How many positive divisors of 2000?

For any primitive pythagorean triple $(a,b,c)$ either $a$ or $b$ must be a multiple of $3$

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