Question

How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?

score 4.8k · Answer 1 · 2011-09-05 19:33:10

4.8k

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How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?

Published on 05 Sep 2011 - 19:33

score 2.6k · Answer 2 · 2026-04-03 15:12:34

2.6k

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How to use fundamental theorem of arithmetic to conclude that $\gcd(a^k,b^n)=1$ for all $k, n \in$ N whenever $a,b \in$ N with $\gcd(a,b)=1$?

Published on 03 Apr 2026 - 15:12

score 302 · Answer 3 · 2011-09-30 00:16:41

302

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$\gcd(a,b) =ax\!+\!by\Rightarrow \gcd(x,y)\!=\!1;\ $ $\gcd(a,b)\gcd(x,y)\mid ax\!+\!by$

Published on 30 Sep 2011 - 0:16

score 8.3k · Answer 4 · 2011-10-25 08:01:31

8.3k

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How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?

Published on 25 Oct 2011 - 8:01

score 1k · Answer 5 · 2011-11-02 16:48:19

1k

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Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$

Published on 02 Nov 2011 - 16:48

score 36.8k · Answer 6 · 2011-11-15 13:00:53

36.8k

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How to calculate GCD of Gaussian integers?

Published on 15 Nov 2011 - 13:00

score 5.1k · Answer 7 · 2026-03-26 12:48:26

5.1k

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Motivation behind the definition of GCD and LCM

Published on 26 Mar 2026 - 12:48

score 34.5k · Answer 8 · 2026-03-29 05:42:56

34.5k

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How to use the Extended Euclidean Algorithm manually?

Published on 29 Mar 2026 - 5:42

score 24.5k · Answer 9 · 2012-01-02 13:04:21

24.5k

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Why $\gcd(b,qb+r)=\gcd(b,r),\,$ so $\,\gcd(b,a) = \gcd(b,a\bmod b)$

Published on 02 Jan 2012 - 13:04

score 8.1k · Answer 10 · 2012-02-16 04:29:39

8.1k

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Showing $\gcd(n^3 + 1, n^2 + 2) = 1$, $3$, or $9$

Published on 16 Feb 2012 - 4:29

score 9.9k · Answer 11 · 2012-02-24 06:51:33

9.9k

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GCD Proof with Multiplication: gcd(ax,bx) = x$\cdot$gcd(a,b)

Published on 24 Feb 2012 - 6:51

score 719 · Answer 12 · 2012-03-15 02:29:41

719

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Stuck computing the gcd $ (n!+1,n+1)$, while computing $(n!+1,(n+1)!)$

Published on 15 Mar 2012 - 2:29

score 2.6k · Answer 13 · 2026-04-04 10:15:59

2.6k

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Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$

Published on 04 Apr 2026 - 10:15

score 1.8k · Answer 14 · 2012-04-25 18:13:10

1.8k

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If $m$ and $n$ are positive integers, then $(F_m,F_n)=F_{(m,n)}$.

Published on 25 Apr 2012 - 18:13

score 1.6k · Answer 15 · 2012-05-14 16:01:08

1.6k

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Relating $\operatorname{lcm}$ and $\gcd$ using inverses or fractions

Published on 14 May 2012 - 16:01

List Question

How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?

How to use fundamental theorem of arithmetic to conclude that $\gcd(a^k,b^n)=1$ for all $k, n \in$ N whenever $a,b \in$ N with $\gcd(a,b)=1$?

$\gcd(a,b) =ax\!+\!by\Rightarrow \gcd(x,y)\!=\!1;\ $ $\gcd(a,b)\gcd(x,y)\mid ax\!+\!by$

How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?

Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$

How to calculate GCD of Gaussian integers?

Motivation behind the definition of GCD and LCM

How to use the Extended Euclidean Algorithm manually?

Why $\gcd(b,qb+r)=\gcd(b,r),\,$ so $\,\gcd(b,a) = \gcd(b,a\bmod b)$

Showing $\gcd(n^3 + 1, n^2 + 2) = 1$, $3$, or $9$

GCD Proof with Multiplication: gcd(ax,bx) = x$\cdot$gcd(a,b)

Stuck computing the gcd $ (n!+1,n+1)$, while computing $(n!+1,(n+1)!)$

Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$

If $m$ and $n$ are positive integers, then $(F_m,F_n)=F_{(m,n)}$.

Relating $\operatorname{lcm}$ and $\gcd$ using inverses or fractions

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