List questions from gcd-and-lcm

Published on 22 Oct 2013 - 21:10

3.3k

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$\gcd(ab,c)$ equals $\gcd(a,c)$ times $\gcd( b, c)$

Published on 23 Oct 2013 - 4:34

34.9k

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How to find the LCM of One Negative and one positive Integer

Published on 27 Oct 2013 - 16:31

92

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Prove that $n$ is prime $\iff \forall a\in\mathbb{Z}(\gcd(a,n)=1\lor n\mid a)$

Published on 30 Oct 2013 - 13:54

244

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How to prove that for all positive integers $a,b$, if $a|b$ , then $\gcd(a,b) = a$?

Published on 12 Nov 2013 - 19:44

3.3k

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Showing $\gcd(2^m-1,2^n+1)=1$

Published on 18 Nov 2013 - 19:06

9.4k

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

Published on 30 Nov 2013 - 6:03

188

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A question on greatest common divisor

Published on 01 Dec 2013 - 15:03

124

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Prove that $\gcd(p + q, p - q) = 2$ if $p$ and $q$ are odd primes

Published on 02 Dec 2013 - 3:38

4.7k

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For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $

Published on 06 Dec 2013 - 5:08

1.6k

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How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$

Published on 17 Dec 2013 - 2:29

3.5k

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Extended Euclidean Algorithm: backward and forward form

Published on 28 Mar 2026 - 15:12

3.4k

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$\gcd(a,b,c)\!=\!1\Rightarrow \gcd(az+b,c)\!=\! 1$ for some $z$ [Coprime Dirichlet Theorem]

Published on 22 Jan 2014 - 15:44

7.6k

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Suppose $(a,b)=1$, then $(2a+b,a+2b)=1\text{ or }3$.

Published on 24 Jan 2014 - 0:44

2.2k

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Greatest common divisor is the smallest positive number that can be written as $sa+tb$

Published on 05 Feb 2014 - 1:49

List Question

Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$

$\gcd(ab,c)$ equals $\gcd(a,c)$ times $\gcd( b, c)$

How to find the LCM of One Negative and one positive Integer

Prove that $n$ is prime $\iff \forall a\in\mathbb{Z}(\gcd(a,n)=1\lor n\mid a)$

How to prove that for all positive integers $a,b$, if $a|b$ , then $\gcd(a,b) = a$?

Showing $\gcd(2^m-1,2^n+1)=1$

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

A question on greatest common divisor

Prove that $\gcd(p + q, p - q) = 2$ if $p$ and $q$ are odd primes

For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $

How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$

Extended Euclidean Algorithm: backward and forward form

$\gcd(a,b,c)\!=\!1\Rightarrow \gcd(az+b,c)\!=\! 1$ for some $z$ [Coprime Dirichlet Theorem]

Suppose $(a,b)=1$, then $(2a+b,a+2b)=1\text{ or }3$.

Greatest common divisor is the smallest positive number that can be written as $sa+tb$

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