List questions from gcd-and-lcm

Published on 23 Feb 2026 - 1:01

6.9k

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If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$

Published on 10 Sep 2014 - 3:30

282

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How do you make the coefficients of the simple linear combination of the gcd positive?

Published on 17 Sep 2014 - 6:26

95

Views

General Rule for calculating solutions to $ax+by=1$ where $(a,b)=1$

Published on 23 Sep 2014 - 19:19

621

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when ${\rm gcd} (a,b)=1$, what is ${\rm gcd} (a+b , a^2+b^2)$?

Published on 07 Oct 2014 - 15:45

751

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Homework gcd. Show that $\gcd(a_1,a_2,a_3,...a_k) = \gcd(\gcd(a_1,a_2),a_3,...a_k)$

Published on 08 Oct 2014 - 19:01

1.7k

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Evaluate $\gcd(ab,p^4)$ and $\gcd(a+b,p^4)$, given that $\gcd(a,p^2)=p$ and $\gcd(b,p^3)=p^2$, where $p$ is a prime.

Published on 08 Oct 2014 - 20:21

945

Views

If $\gcd(\gcd(a, b),\gcd(a, c))=1$, then $\gcd(a, bc) = \gcd(a, b) \cdot \gcd(a, c)$

Published on 17 Oct 2014 - 1:59

3k

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The greatest common divisor is the smallest positive linear combination

Published on 19 Oct 2014 - 4:40

1.2k

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For every natural number $n$, $\gcd(an,bn)=n\gcd(a,b).$

Published on 20 Oct 2014 - 16:35

18.1k

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

Published on 24 Oct 2014 - 5:58

250

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Prove $\langle a^s \rangle=\langle a^t \rangle \iff \gcd(n,s)=\gcd(n,t)$

Published on 11 Nov 2014 - 6:27

167

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GCD Direct Proof

Published on 23 Nov 2014 - 22:35

2.2k

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Prove GCD of polynomials is same when coefficients are in a different field

Published on 11 Dec 2014 - 3:16

98

Views

Greatest Common Divisor multiplicative proof

Published on 02 Oct 2019 - 8:56

List Question

May I have a hint for this gcd problem?

If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$

How do you make the coefficients of the simple linear combination of the gcd positive?

General Rule for calculating solutions to $ax+by=1$ where $(a,b)=1$

when ${\rm gcd} (a,b)=1$, what is ${\rm gcd} (a+b , a^2+b^2)$?

Homework gcd. Show that $\gcd(a_1,a_2,a_3,...a_k) = \gcd(\gcd(a_1,a_2),a_3,...a_k)$

Evaluate $\gcd(ab,p^4)$ and $\gcd(a+b,p^4)$, given that $\gcd(a,p^2)=p$ and $\gcd(b,p^3)=p^2$, where $p$ is a prime.

If $\gcd(\gcd(a, b),\gcd(a, c))=1$, then $\gcd(a, bc) = \gcd(a, b) \cdot \gcd(a, c)$

The greatest common divisor is the smallest positive linear combination

For every natural number $n$, $\gcd(an,bn)=n\gcd(a,b).$

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

Prove $\langle a^s \rangle=\langle a^t \rangle \iff \gcd(n,s)=\gcd(n,t)$

GCD Direct Proof

Prove GCD of polynomials is same when coefficients are in a different field

Greatest Common Divisor multiplicative proof

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