Question

Prove the order of the group homomorphism of an element divides the order of the element.

score 1.9k · Answer 1 · 2026-03-31 03:39:06

1.9k

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Prove the order of the group homomorphism of an element divides the order of the element.

Published on 31 Mar 2026 - 3:39

score 670 · Answer 2 · 2026-04-02 17:51:10

670

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Find $GCD(n^2+1,n+1)$

Published on 02 Apr 2026 - 17:51

score 660 · Answer 3 · 2026-03-31 20:53:39

660

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Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$

Published on 31 Mar 2026 - 20:53

score 93 · Answer 4 · 2015-04-16 05:06:21

93

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$5 \nmid 2^{n}-1$ when $n$ is odd

Published on 16 Apr 2015 - 5:06

score 56 · Answer 5 · 2015-04-16 21:35:44

56

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Decide if there exist $a$ and $b \in \mathbb{Z}$ such that $a^2=2b^2$.

Published on 16 Apr 2015 - 21:35

score 277 · Answer 6 · 2015-04-17 05:28:16

277

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Proving $k$ is divisible by $3$ iff the sum of the digits of $k$ is divisible by 3

Published on 17 Apr 2015 - 5:28

score 585 · Answer 7 · 2015-04-17 23:11:30

585

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Mathematical induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$

Published on 17 Apr 2015 - 23:11

score 3.3k · Answer 8 · 2026-04-09 09:19:25

3.3k

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Pythagorean Triples : Show that exactly one of $x$, $y$, and $z$ is divisible by $5$

Published on 09 Apr 2026 - 9:19

score 2.2k · Answer 9 · 2026-03-27 13:47:21

2.2k

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Pythagorean Triples : Is every positive integer $\gt$ $2$ part of at least one Pythagorean triple?

Published on 27 Mar 2026 - 13:47

score 66 · Answer 10 · 2026-03-26 19:06:43

66

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An expression with gcd and abs is transformed magically!

Published on 26 Mar 2026 - 19:06

score 247 · Answer 11 · 2026-04-11 19:03:37

247

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Fermat's Little Theorem and prime divisors

Published on 11 Apr 2026 - 19:03

score 739 · Answer 12 · 2026-03-29 07:40:26

739

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Example of a domain where all irreducibles are primes and that is not a GCD domain

Published on 29 Mar 2026 - 7:40

score 36 · Answer 13 · 2015-04-21 19:17:30

36

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Prove that if $a, b, n\in \mathbb{N}, n\geq2\longrightarrow \sqrt[\leftroot{-2}\uproot{2}n]{a}\in \mathbb{Q} \iff a=b^n$.

Published on 21 Apr 2015 - 19:17

score 238 · Answer 14 · 2015-04-22 14:52:11

238

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Suppose $p$ is a prime number and $a$ is an integer. Show that if $p \mid a^n$, then $p^n \mid a^n$ for any $n \geq 1$?

Published on 22 Apr 2015 - 14:52

score 2.9k · Answer 15 · 2015-04-22 22:01:00

2.9k

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GCD theory - gcd(x, y) = 1

Published on 22 Apr 2015 - 22:01

List Question

Prove the order of the group homomorphism of an element divides the order of the element.

Find $GCD(n^2+1,n+1)$

Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$

$5 \nmid 2^{n}-1$ when $n$ is odd

Decide if there exist $a$ and $b \in \mathbb{Z}$ such that $a^2=2b^2$.

Proving $k$ is divisible by $3$ iff the sum of the digits of $k$ is divisible by 3

Mathematical induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$

Pythagorean Triples : Show that exactly one of $x$, $y$, and $z$ is divisible by $5$

Pythagorean Triples : Is every positive integer $\gt$ $2$ part of at least one Pythagorean triple?

An expression with gcd and abs is transformed magically!

Fermat's Little Theorem and prime divisors

Example of a domain where all irreducibles are primes and that is not a GCD domain

Prove that if $a, b, n\in \mathbb{N}, n\geq2\longrightarrow \sqrt[\leftroot{-2}\uproot{2}n]{a}\in \mathbb{Q} \iff a=b^n$.

Suppose $p$ is a prime number and $a$ is an integer. Show that if $p \mid a^n$, then $p^n \mid a^n$ for any $n \geq 1$?

GCD theory - gcd(x, y) = 1

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