Question

Addition or subtraction in GCD and LCM

score 2.5k · Answer 1 · 2012-10-22 19:34:09

2.5k

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Addition or subtraction in GCD and LCM

Published on 22 Oct 2012 - 19:34

score 16.6k · Answer 2 · 2012-10-24 07:30:21

16.6k

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Is greatest common divisor of two numbers really their smallest linear combination?

Published on 24 Oct 2012 - 7:30

score 17.7k · Answer 3 · 2026-02-23 08:39:34

17.7k

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Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$

Published on 23 Feb 2026 - 8:39

score 2.3k · Answer 4 · 2012-11-07 03:39:27

2.3k

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Prove that for any integer $k \ne 0$, $\gcd(k, k+1) = 1$

Published on 07 Nov 2012 - 3:39

score 12.3k · Answer 5 · 2026-02-24 13:35:44

12.3k

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Prove the LCM (Least Common Multiple).

Published on 24 Feb 2026 - 13:35

score 3.1k · Answer 6 · 2012-11-29 09:48:55

3.1k

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Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$

Published on 29 Nov 2012 - 9:48

score 147 · Answer 7 · 2012-11-30 15:15:32

147

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How to show that: $ \gcd \Big(2^{2^a}+1 , 2^{2^b}+1\Big)=1$

Published on 30 Nov 2012 - 15:15

score 1.7k · Answer 8 · 2012-12-07 01:39:25

1.7k

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Euclid's Lemma $\,(a,b)=1,\ a\mid bc\Rightarrow a\mid c\,$ in Bezout, gcd, ideal form

Published on 07 Dec 2012 - 1:39

score 3.2k · Answer 9 · 2012-12-09 17:38:37

3.2k

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LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$

Published on 09 Dec 2012 - 17:38

score 11.1k · Answer 10 · 2012-12-12 20:13:11

11.1k

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If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.

Published on 12 Dec 2012 - 20:13

score 15k · Answer 11 · 2026-02-23 19:19:46

15k

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If $(a,b)=1$ then prove $(a+b, ab)=1$.

Published on 23 Feb 2026 - 19:19

score 845 · Answer 12 · 2013-01-15 22:22:06

845

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Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$

Published on 15 Jan 2013 - 22:22

score 15.6k · Answer 13 · 2026-04-02 09:27:30

15.6k

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If a and b are relatively prime and ab is a square, then a and b are squares.

Published on 02 Apr 2026 - 9:27

score 22.6k · Answer 14 · 2013-01-28 02:42:36

22.6k

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

Published on 28 Jan 2013 - 2:42

score 1.1k · Answer 15 · 2013-02-11 15:09:12

1.1k

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Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$

Published on 11 Feb 2013 - 15:09

List Question

Addition or subtraction in GCD and LCM

Is greatest common divisor of two numbers really their smallest linear combination?

Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$

Prove that for any integer $k \ne 0$, $\gcd(k, k+1) = 1$

Prove the LCM (Least Common Multiple).

Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$

How to show that: $ \gcd \Big(2^{2^a}+1 , 2^{2^b}+1\Big)=1$

Euclid's Lemma $\,(a,b)=1,\ a\mid bc\Rightarrow a\mid c\,$ in Bezout, gcd, ideal form

LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$

If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.

If $(a,b)=1$ then prove $(a+b, ab)=1$.

Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$

If a and b are relatively prime and ab is a square, then a and b are squares.

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

Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$

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