List questions from divisibility

Published on 28 Mar 2026 - 20:14

145

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Prove that if $m\mid z$ implies that $n \mid z$, then $n\mid m$

Published on 18 Feb 2020 - 11:07

232

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Prove if $5 \nmid n$, then $n^2 = 5k \pm 1$

Published on 29 Mar 2026 - 17:24

105

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Let $n\in\Bbb Z$. Prove that $n$ is a multiple of both $5$ and $9$ if and only if it is a multiple of $45$.

Published on 29 Mar 2026 - 19:14

105

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Is it possible to derive $m < p^k$ from the Diophantine equation $m^2 - p^k = 4z$ unconditionally, when it is solvable?

Published on 26 Mar 2026 - 0:53

53

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Help with induction using divisibility.

Published on 22 Feb 2020 - 8:33

54

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Question regarding $\gcd(a,b)=\gcd(b,r)$

Published on 29 Mar 2026 - 2:45

765

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Divisibility rule for large primes

Published on 23 Feb 2020 - 12:35

32

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What's wrong with this (very simple) divisibility proof?

Published on 23 Feb 2020 - 18:46

755

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Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Published on 27 Mar 2026 - 13:48

75

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Prove that there exists $a_1, b_1 \in \mathbb{Z}$ such that $d = a_1 b_1$ and $a_1 \mid a$ and $b_1 \mid b$.

Published on 24 Feb 2020 - 11:19

1k

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Proof by induction: $2^{2n}-1$ is a multiple of $3$

Published on 26 Feb 2020 - 8:16

123

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if $x$ is odd, show that $x^3+x$ has a remainder 2 when divided by 4

Published on 27 Feb 2020 - 2:10

1.1k

Views

7 digit number combinations

Published on 27 Feb 2020 - 16:40

82

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How to completely factor $x^{\varphi(a)} - 1$ when $\gcd(a,x)=1$?

Published on 27 Mar 2026 - 15:16

List Question

Prove $\gcd(a^n,b^n) = 1 \Rightarrow \gcd(a,b)=1$

Prove that if $m\mid z$ implies that $n \mid z$, then $n\mid m$

Prove if $5 \nmid n$, then $n^2 = 5k \pm 1$

Let $n\in\Bbb Z$. Prove that $n$ is a multiple of both $5$ and $9$ if and only if it is a multiple of $45$.

Is it possible to derive $m < p^k$ from the Diophantine equation $m^2 - p^k = 4z$ unconditionally, when it is solvable?

Help with induction using divisibility.

Question regarding $\gcd(a,b)=\gcd(b,r)$

Divisibility rule for large primes

What's wrong with this (very simple) divisibility proof?

Let $p$ be an odd prime and let $m = 2p$. Prove that $a^{m−1} ≡ a \pmod{m}$ for all natural numbers $a$.

Prove that there exists $a_1, b_1 \in \mathbb{Z}$ such that $d = a_1 b_1$ and $a_1 \mid a$ and $b_1 \mid b$.

Proof by induction: $2^{2n}-1$ is a multiple of $3$

if $x$ is odd, show that $x^3+x$ has a remainder 2 when divided by 4

7 digit number combinations

How to completely factor $x^{\varphi(a)} - 1$ when $\gcd(a,x)=1$?

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