List questions from gcd-and-lcm

Published on 01 Aug 2013 - 14:49

110

Views

If $a,b,x,y\in\Bbb N$ , and $ax-by=(a,b)$, then $(x,y)=1$

Published on 04 Aug 2013 - 22:29

257

Views

prove $a,b,c \in\mathbb{Z}$ Show that $\gcd(a,b)=1$ and $\gcd(a,c)=1$ iff $\gcd(a,[b,c])=1$

Published on 05 Aug 2013 - 5:42

990

Views

Prove that if $\gcd(n, m) = 1$, then $\gcd(R_n, R_m) = 1$

Published on 24 Aug 2013 - 8:17

2.5k

Views

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Published on 28 Aug 2013 - 6:58

15.3k

Views

Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$

Published on 05 Sep 2013 - 16:44

394

Views

If $a \mid c$ and $b \mid c$, but $\gcd(a,b) = 1$, then $ab \mid c$.

Published on 02 Apr 2026 - 7:58

27.6k

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What is $\gcd(0,0)$?

Published on 16 Sep 2013 - 4:53

315

Views

If $ a \mid bc $ then $\frac{a}{\gcd(a,b)} \mid c$?

Published on 28 Sep 2013 - 18:29

21.2k

Views

Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$

Published on 03 Oct 2013 - 2:31

1.2k

Views

Distinct Mersenne numbers are coprime

Published on 23 Feb 2026 - 6:36

18.5k

Views

Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)

Published on 03 Oct 2013 - 22:33

246

Views

Proof $\displaystyle \text{lcm}(x,y)=\frac{|x\cdot y|}{\text{gcd}(x,y)}$

Published on 20 Oct 2013 - 16:07

70

Views

straightforward hcf question

Published on 20 Oct 2013 - 17:29

1.1k

Views

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

Published on 22 Oct 2013 - 18:18

List Question

Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$

If $a,b,x,y\in\Bbb N$ , and $ax-by=(a,b)$, then $(x,y)=1$

prove $a,b,c \in\mathbb{Z}$ Show that $\gcd(a,b)=1$ and $\gcd(a,c)=1$ iff $\gcd(a,[b,c])=1$

Prove that if $\gcd(n, m) = 1$, then $\gcd(R_n, R_m) = 1$

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$

If $a \mid c$ and $b \mid c$, but $\gcd(a,b) = 1$, then $ab \mid c$.

What is $\gcd(0,0)$?

If $ a \mid bc $ then $\frac{a}{\gcd(a,b)} \mid c$?

Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$

Distinct Mersenne numbers are coprime

Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)

Proof $\displaystyle \text{lcm}(x,y)=\frac{|x\cdot y|}{\text{gcd}(x,y)}$

straightforward hcf question

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

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