Question

Prove that $\gcd(a,b)=d \Rightarrow \gcd(p^a-1,p^b-1)=p^d-1$

score 69 · Answer 1 · 2017-07-06 08:52:13

69

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Prove that $\gcd(a,b)=d \Rightarrow \gcd(p^a-1,p^b-1)=p^d-1$

Published on 06 Jul 2017 - 8:52

score 48 · Answer 2 · 2017-07-06 19:31:01

48

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$\gcd=1$ if $ m^n=ab \Rightarrow m^n=(a'b')^n$?

Published on 06 Jul 2017 - 19:31

score 757 · Answer 3 · 2026-02-23 17:24:53

757

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CoPrimes of Large Numbers

Published on 23 Feb 2026 - 17:24

score 270 · Answer 4 · 2017-07-10 05:57:23

270

Views

Let $a,b,c,d$ be positive integers such that $ab=cd$. Prove that $\gcd(a,c)\gcd(a,d) = a\gcd(a,b,c,d).$

Published on 10 Jul 2017 - 5:57

score 1.9k · Answer 5 · 2017-07-13 15:23:44

1.9k

Views

Does the Bezout GCD equation hold in a UFD?

Published on 13 Jul 2017 - 15:23

score 61 · Answer 6 · 2017-07-16 17:27:39

61

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If $a\mid d$, $b\mid d$, $a=u\cdot\gcd(a, b)$ and $b=v\cdot\gcd(a, b)$, then there is an integer $r$ such that $d=ruv\cdot GCD(a, b)$

Published on 16 Jul 2017 - 17:27

score 689 · Answer 7 · 2017-07-18 19:26:00

689

Views

GCD of two polynomials without Euclidean algorithm

Published on 18 Jul 2017 - 19:26

score 398 · Answer 8 · 2017-07-20 21:53:37

398

Views

Proof that $Z$ is a gcd ring

Published on 20 Jul 2017 - 21:53

score 297 · Answer 9 · 2017-07-21 07:45:59

297

Views

Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$

Published on 21 Jul 2017 - 7:45

score 1.3k · Answer 10 · 2026-03-28 11:53:37

1.3k

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Example of a non-gcd domain

Published on 28 Mar 2026 - 11:53

score 3.8k · Answer 11 · 2017-07-30 18:04:15

3.8k

Views

Closest divisor

Published on 30 Jul 2017 - 18:04

score 38 · Answer 12 · 2017-07-30 21:12:12

38

Views

If $(-1)^{\gcd(n,F_n)}=1$ where $F_n$ is the $n$-th Fibonacci number then $n$ is divisible by $6$ ?

Published on 30 Jul 2017 - 21:12

score 586 · Answer 13 · 2017-07-30 23:39:08

586

Views

Find the maximum positive integer that divides $n^7+n^6-n^5-n^4$

Published on 30 Jul 2017 - 23:39

score 474 · Answer 14 · 2017-08-02 09:17:40

474

Views

Understanding proof that involves gcd and linear combinations

Published on 02 Aug 2017 - 9:17

score 2.3k · Answer 15 · 2017-08-05 07:34:40

2.3k

Views

Prove that$\gcd(a+b, a-b) = \gcd(2a, a-b) = \gcd(a+b, 2b) $

Published on 05 Aug 2017 - 7:34

List Question

Prove that $\gcd(a,b)=d \Rightarrow \gcd(p^a-1,p^b-1)=p^d-1$

$\gcd=1$ if $ m^n=ab \Rightarrow m^n=(a'b')^n$?

CoPrimes of Large Numbers

Let $a,b,c,d$ be positive integers such that $ab=cd$. Prove that $\gcd(a,c)\gcd(a,d) = a\gcd(a,b,c,d).$

Does the Bezout GCD equation hold in a UFD?

If $a\mid d$, $b\mid d$, $a=u\cdot\gcd(a, b)$ and $b=v\cdot\gcd(a, b)$, then there is an integer $r$ such that $d=ruv\cdot GCD(a, b)$

GCD of two polynomials without Euclidean algorithm

Proof that $Z$ is a gcd ring

Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$

Example of a non-gcd domain

Closest divisor

If $(-1)^{\gcd(n,F_n)}=1$ where $F_n$ is the $n$-th Fibonacci number then $n$ is divisible by $6$ ?

Find the maximum positive integer that divides $n^7+n^6-n^5-n^4$

Understanding proof that involves gcd and linear combinations

Prove that$\gcd(a+b, a-b) = \gcd(2a, a-b) = \gcd(a+b, 2b) $

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