List questions from divisibility

Published on 08 Apr 2026 - 14:10

340

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How can I prove that if $a^7 = b^7$ then $a=b$, with $ a,b \in \mathbb{Z} $

Published on 13 Apr 2026 - 5:35

3.3k

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How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

Published on 14 Apr 2026 - 23:59

44

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When $n\mid\sum_{k=1}^{n}\phi (k)$

Published on 29 Mar 2026 - 17:31

118

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Let $p \in \mathbb{Z}$ so that if for all $a,b \in \mathbb{Z}$ where $p \mid (ab)$ is true then $p \mid a$ or $p \mid b$. Does this makes $p$ a prime?

Published on 14 Apr 2026 - 5:40

413

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Probability that $7^m+7^n$ is divisible by $5$

Published on 12 Apr 2026 - 7:45

1.5k

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Prove that $8640$ divides $n^9 - 6n^7 + 9n^5 - 4n^3$.

Published on 14 Apr 2026 - 23:26

1.9k

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Prove that $6$ divides $n^3+11n$?

Published on 14 Apr 2026 - 20:18

129

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a number n as pa+qb

Published on 13 Apr 2026 - 14:25

234

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When does $\phi (n) \mid n $?

Published on 29 Mar 2026 - 17:23

1000

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Divisibility of Binomial Coefficients by a Composite Number

Published on 13 Apr 2026 - 23:00

795

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proof - GCD and Number Theory

Published on 12 Apr 2026 - 23:36

34

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Confused about a simplification step in induction

Published on 12 Apr 2026 - 7:25

126

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Reference request for a divisibility property of Fibonacci numbers

Published on 14 Apr 2026 - 7:08

67

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The primes $2s+1$ with the constraint that $s$ satisfy certain congruence relations and Euler's idoneal numbers.

Published on 14 Apr 2026 - 13:03

List Question

Finding Divisibility of Sequence of Numbers Generated Recursively

How can I prove that if $a^7 = b^7$ then $a=b$, with $ a,b \in \mathbb{Z} $

How to solve these two simultaneous "divisibilities" : $n+1\mid m^2+1$ and $m+1\mid n^2+1$

When $n\mid\sum_{k=1}^{n}\phi (k)$

Let $p \in \mathbb{Z}$ so that if for all $a,b \in \mathbb{Z}$ where $p \mid (ab)$ is true then $p \mid a$ or $p \mid b$. Does this makes $p$ a prime?

Probability that $7^m+7^n$ is divisible by $5$

Prove that $8640$ divides $n^9 - 6n^7 + 9n^5 - 4n^3$.

Prove that $6$ divides $n^3+11n$?

a number n as pa+qb

When does $\phi (n) \mid n $?

Divisibility of Binomial Coefficients by a Composite Number

proof - GCD and Number Theory

Confused about a simplification step in induction

Reference request for a divisibility property of Fibonacci numbers

The primes $2s+1$ with the constraint that $s$ satisfy certain congruence relations and Euler's idoneal numbers.

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