List questions from divisibility

Published on 20 Aug 2016 - 9:48

51

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Proof verification - working with integers

Published on 03 Apr 2026 - 21:40

57

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Residue of $n$ given residue of $4n$

Published on 20 Aug 2016 - 20:05

1.3k

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A divisibility rule for 19

Published on 20 Aug 2016 - 20:12

2.1k

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Prove that :- $A_n = 2903^n - 803^n - 464^n + 261^n$ is divisible by $1897$ for $n \in \mathbb{N}$

Published on 20 Aug 2016 - 20:21

404

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Find every pair of integers $(p,q)$ such that $ \frac {p^3 -q}{pq+1} $ is an integer

Published on 31 Mar 2026 - 3:58

71

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Prove that $(2n-1)(3^n)+1$ is always divisible by 4.

Published on 23 Aug 2016 - 15:08

98

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$a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$.

Published on 24 Aug 2016 - 6:43

900

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Shortcut to find remainder (mod) of a number to a negative power?

Published on 24 Aug 2016 - 15:51

288

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Divisors of $10^{100} -1$

Published on 29 Mar 2026 - 22:14

261

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Prove $\forall n\ge 2, 2^{n}-1 \nmid \ 3^{n}-1$

Published on 25 Aug 2016 - 10:00

7.6k

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What is the smallest positive multiple of 450 whose digits are all zeroes and ones?

Published on 26 Mar 2026 - 14:22

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Show that $n(2n + 1)(7n + 1)$ is divisible by 6 for all integers $n$ and find all integers $n$ such that $n(2n + 1)(7n + 1)$ is divisible by 12.

Published on 25 Aug 2016 - 22:26

1k

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Prove by mathematical induction that $31\mid5^{n+1}+6^{2n-1},\;$ $\forall n \in \mathbb{N}$

Published on 26 Aug 2016 - 9:37

176

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$m+n$ divides $a_m+a_n$

Published on 26 Aug 2016 - 10:52

List Question

For which $(a, b, \mu)$ is $\frac{b^2 - a^2 - 1 - 2a\mu}{2b}$ an integer?

Proof verification - working with integers

Residue of $n$ given residue of $4n$

A divisibility rule for 19

Prove that :- $A_n = 2903^n - 803^n - 464^n + 261^n$ is divisible by $1897$ for $n \in \mathbb{N}$

Find every pair of integers $(p,q)$ such that $ \frac {p^3 -q}{pq+1} $ is an integer

Prove that $(2n-1)(3^n)+1$ is always divisible by 4.

$a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$.

Shortcut to find remainder (mod) of a number to a negative power?

Divisors of $10^{100} -1$

Prove $\forall n\ge 2, 2^{n}-1 \nmid \ 3^{n}-1$

What is the smallest positive multiple of 450 whose digits are all zeroes and ones?

Show that $n(2n + 1)(7n + 1)$ is divisible by 6 for all integers $n$ and find all integers $n$ such that $n(2n + 1)(7n + 1)$ is divisible by 12.

Prove by mathematical induction that $31\mid5^{n+1}+6^{2n-1},\;$ $\forall n \in \mathbb{N}$

$m+n$ divides $a_m+a_n$

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