List questions from divisibility

Published on 08 Jan 2017 - 19:02

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How to prove that gcd(m+1, n+1) divides (mn-1)

Published on 30 Mar 2026 - 17:37

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$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes

Published on 10 Jan 2017 - 3:49

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A simple proof by induction $P(n) = \frac{6^{2n} - 3^n}{11} \in \mathbb{N}$

Published on 10 Jan 2017 - 14:09

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If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.

Published on 10 Jan 2017 - 19:26

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Find all $n$ such that $n \mid 3^n + 1$.

Published on 10 Jan 2017 - 20:17

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Divisibility of the sum of squares of two odd numbers

Published on 28 Mar 2026 - 0:06

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When $p \mid a^2+ab+b^2$?

Published on 12 Jan 2017 - 8:02

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How many numbers can be formed using $1,3,4,5,6,9$ only once and divisible by $7$ or $11$ or $13$?

Published on 12 Jan 2017 - 20:19

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How to find number of steps in Euclidean Algorithm for fibonacci numbers

Published on 29 Mar 2026 - 22:28

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Proof of a certain divisibility property

Published on 14 Jan 2017 - 6:56

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Prove $n$ and $n^2-n+1$ are co-prime.

Published on 14 Jan 2017 - 10:43

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How many such numbers are there?

Published on 14 Jan 2017 - 15:36

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Need to prove divisibility of $7^p-5^p-2$ by $3$ by using Fermat's little Theorem

Published on 14 Jan 2017 - 15:50

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Elementary divisor theorem for integer matrices

Published on 14 Jan 2017 - 17:23

List Question

If $ x_1=2$ and $x_{n+1}=2^{x_n}-1$ then $x_n$ divides $2^{x_n}-2$

How to prove that gcd(m+1, n+1) divides (mn-1)

$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes

A simple proof by induction $P(n) = \frac{6^{2n} - 3^n}{11} \in \mathbb{N}$

If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.

Find all $n$ such that $n \mid 3^n + 1$.

Divisibility of the sum of squares of two odd numbers

When $p \mid a^2+ab+b^2$?

How many numbers can be formed using $1,3,4,5,6,9$ only once and divisible by $7$ or $11$ or $13$?

How to find number of steps in Euclidean Algorithm for fibonacci numbers

Proof of a certain divisibility property

Prove $n$ and $n^2-n+1$ are co-prime.

How many such numbers are there?

Need to prove divisibility of $7^p-5^p-2$ by $3$ by using Fermat's little Theorem

Elementary divisor theorem for integer matrices

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