List questions from gcd-and-lcm

Published on 01 Mar 2011 - 0:53

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Prove that any two consecutive terms of the Fibonacci sequence are relatively prime

Published on 01 Mar 2011 - 7:19

10.8k

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Proving that $\gcd(ac,bc)=|c|\gcd(a,b)$

Published on 06 Mar 2011 - 1:26

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Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$

Published on 03 Apr 2026 - 6:40

8.4k

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Prove that $\gcd(n!+1,(n+1)!+1)=1$

Published on 08 Mar 2011 - 2:49

5.2k

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Basis for $\mathbb{Z}^2$

Published on 17 Mar 2011 - 15:44

52.8k

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What is $\gcd(0,a)$, where $a$ is a positive integer?

Published on 18 Mar 2011 - 2:34

51.9k

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Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$

Published on 13 Apr 2011 - 11:22

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Integral domain with two elements that do not have a gcd

Published on 05 May 2011 - 2:16

856

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Is Gauss's lemma valid for polynomials with coefficients in a GCD domain?

Published on 09 May 2011 - 20:19

4.7k

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For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$

Published on 24 Feb 2026 - 13:37

2.3k

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Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$

Published on 19 Jul 2011 - 10:23

1.5k

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Simple example of non-arithmetic ring (non-distributive ideal lattice)

Published on 02 Apr 2026 - 4:28

14.3k

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Fibonacci divisibility properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$

Published on 28 Aug 2011 - 15:32

484

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Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$

Published on 05 Sep 2011 - 18:20

List Question

Prove that $\gcd( a + a', b + b' ) = 1$ if $ab - a'b' = \pm 1$

Prove that any two consecutive terms of the Fibonacci sequence are relatively prime

Proving that $\gcd(ac,bc)=|c|\gcd(a,b)$

Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$

Prove that $\gcd(n!+1,(n+1)!+1)=1$

Basis for $\mathbb{Z}^2$

What is $\gcd(0,a)$, where $a$ is a positive integer?

Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$

Integral domain with two elements that do not have a gcd

Is Gauss's lemma valid for polynomials with coefficients in a GCD domain?

For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$

Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$

Simple example of non-arithmetic ring (non-distributive ideal lattice)

Fibonacci divisibility properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$

Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$

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