Question

If $a,b,c \in \mathbb{Z}$ with $gcd(a,b)=1$ where $ab=c^n$, then $\exists d,e\in \mathbb{N}$, such that $a=d^n$ and $b=e^n$

score 163 · Answer 1 · 2026-04-04 14:17:50

163

Views

If $a,b,c \in \mathbb{Z}$ with $gcd(a,b)=1$ where $ab=c^n$, then $\exists d,e\in \mathbb{N}$, such that $a=d^n$ and $b=e^n$

Published on 04 Apr 2026 - 14:17

score 193 · Answer 2 · 2021-09-30 13:44:11

193

Views

Proof that if $\gcd(a,b)=\gcd(a^2 , b^2)$, then $\gcd(a,b)=1$

Published on 30 Sep 2021 - 13:44

score 177 · Answer 3 · 2021-09-30 16:02:07

177

Views

Proof that if $\gcd(a,b)=1$, then $\gcd(a^2, b^2)=1$

Published on 30 Sep 2021 - 16:02

score 328 · Answer 4 · 2021-10-01 11:21:03

328

Views

How many pairs of numbers are there whose LCM is $200$?

Published on 01 Oct 2021 - 11:21

score 117 · Answer 5 · 2021-10-04 11:14:33

117

Views

Understanding proof of Rosen on GCD of two integers

Published on 04 Oct 2021 - 11:14

score 129 · Answer 6 · 2026-03-30 12:37:01

129

Views

Constructing regular $mn$-gon if $m$-, $n$-gons are constructible

Published on 30 Mar 2026 - 12:37

score 76 · Answer 7 · 2021-10-06 15:03:26

76

Views

Find all natural n such that gcd(n, 1260)=70 and the number of positive divisors of n is 30

Published on 06 Oct 2021 - 15:03

score 306 · Answer 8 · 2021-10-09 16:21:04

306

Views

Proof verification: If $\gcd(n,a) = 1$ and $n\mid ab$ then $n\mid b$.

Published on 09 Oct 2021 - 16:21

score 61 · Answer 9 · 2021-10-10 17:26:02

61

Views

Consequence of Linear Diophantine Equation

Published on 10 Oct 2021 - 17:26

score 217 · Answer 10 · 2021-10-12 19:37:16

217

Views

Expected number of rolls until lcm is greater than $2000$?

Published on 12 Oct 2021 - 19:37

score 47 · Answer 11 · 2021-10-13 15:46:06

47

Views

Help with GCD Coprime Proof

Published on 13 Oct 2021 - 15:46

score 552 · Answer 12 · 2021-10-13 22:24:48

552

Views

Intuitive understanding of Bezout's Identity?

Published on 13 Oct 2021 - 22:24

score 159 · Answer 13 · 2026-03-30 17:11:28

What is an example for a GCD domain that is neither a UFD (like $\Bbb Z[X]$) nor Bézout (like holomorphic functions on all of $\Bbb C$)?

score 28 · Answer 14 · 2021-10-15 12:46:27

Proving uniqueness that if $S = \{as+bt|as+bt>0, a,b \in \Bbb N\}$ and $d, d' \in S$ and $d|a$, $d|b$, $d'|a$, $d'|b$ $\rightarrow$ $d = d'$.

score 428 · Answer 15 · 2021-10-16 09:09:22

428

Views

Prove that if (a,b) are positive integers with gcd(a,bc) = gcd(a,b)gcd(a,c) , then gcd(a,b)=1

Published on 16 Oct 2021 - 9:09

List Question

If $a,b,c \in \mathbb{Z}$ with $gcd(a,b)=1$ where $ab=c^n$, then $\exists d,e\in \mathbb{N}$, such that $a=d^n$ and $b=e^n$

Proof that if $\gcd(a,b)=\gcd(a^2 , b^2)$, then $\gcd(a,b)=1$

Proof that if $\gcd(a,b)=1$, then $\gcd(a^2, b^2)=1$

How many pairs of numbers are there whose LCM is $200$?

Understanding proof of Rosen on GCD of two integers

Constructing regular $mn$-gon if $m$-, $n$-gons are constructible

Find all natural n such that gcd(n, 1260)=70 and the number of positive divisors of n is 30

Proof verification: If $\gcd(n,a) = 1$ and $n\mid ab$ then $n\mid b$.

Consequence of Linear Diophantine Equation

Expected number of rolls until lcm is greater than $2000$?

Help with GCD Coprime Proof

Intuitive understanding of Bezout's Identity?

What is an example for a GCD domain that is neither a UFD (like $\Bbb Z[X]$) nor Bézout (like holomorphic functions on all of $\Bbb C$)?

Proving uniqueness that if $S = \{as+bt|as+bt>0, a,b \in \Bbb N\}$ and $d, d' \in S$ and $d|a$, $d|b$, $d'|a$, $d'|b$ $\rightarrow$ $d = d'$.

Prove that if (a,b) are positive integers with gcd(a,bc) = gcd(a,b)gcd(a,c) , then gcd(a,b)=1

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