List questions from gcd-and-lcm

Published on 29 Jun 2016 - 8:58

129

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Prove that $\operatorname {gcd}(\operatorname {gcd}(m,n), p) = \operatorname {gcd}(m,\operatorname {gcd}(n, p))$

Published on 02 Jul 2016 - 7:51

1.6k

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$\text{lcm}(a,b)\cdot\text{lcm}(b,c)\cdot\text{lcm}(c,a)=a\cdot b\cdot c\cdot\text{gcd}(a,b,c)$,none a,b,c is integer multiple of any other of a,b,c.

Published on 05 Jul 2016 - 0:22

441

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The Greatest Common Divisor of All Numbers of the Form $n^a-n^b$

Published on 02 Apr 2026 - 1:28

304

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Entries of the inverse of $\left[\frac{1}{x+i+j-1}\right]_{i,j\in\{1,2,\ldots,n\}}$ are polynomials in $x$.

Published on 02 Apr 2026 - 10:15

19.1k

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Euclidean Algorithm for GCD of polynomials

Published on 05 Apr 2013 - 12:28

20.9k

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Concise proof that every common divisor divides GCD without Bezout's identity?

Published on 16 Apr 2013 - 2:18

6.7k

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Bezout's identity in $F[x]$

Published on 17 Apr 2013 - 20:44

279

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Finding numbers from LCM and HCF

Published on 24 Feb 2026 - 5:32

567

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Euclidean algorithm for $\gcd(60,17)$

Published on 28 Mar 2026 - 15:10

55.9k

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If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]

Published on 11 Jun 2013 - 14:14

2k

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Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.

Published on 02 Jul 2013 - 2:48

60

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Show that if $b\mid c$ and $b > \gcd(c, d)$, then $b\nmid d$.

Published on 08 Jul 2013 - 16:49

414

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Prove that MCD is 1 or 3 knowing (a,b) = 1

Published on 15 Jul 2013 - 3:05

141

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Prove $m=[a,b]\Longleftrightarrow \left(\frac{m}{a},\frac{m}{b}\right)=1$

Published on 24 Feb 2026 - 5:36

List Question

How to prove $\gcd(a-bc, b) =\gcd(a,b)$ for $a,b,c \in \mathbb{Z}$?

Prove that $\operatorname {gcd}(\operatorname {gcd}(m,n), p) = \operatorname {gcd}(m,\operatorname {gcd}(n, p))$

$\text{lcm}(a,b)\cdot\text{lcm}(b,c)\cdot\text{lcm}(c,a)=a\cdot b\cdot c\cdot\text{gcd}(a,b,c)$,none a,b,c is integer multiple of any other of a,b,c.

The Greatest Common Divisor of All Numbers of the Form $n^a-n^b$

Entries of the inverse of $\left[\frac{1}{x+i+j-1}\right]_{i,j\in\{1,2,\ldots,n\}}$ are polynomials in $x$.

Euclidean Algorithm for GCD of polynomials

Concise proof that every common divisor divides GCD without Bezout's identity?

Bezout's identity in $F[x]$

Finding numbers from LCM and HCF

Euclidean algorithm for $\gcd(60,17)$

If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]

Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.

Show that if $b\mid c$ and $b > \gcd(c, d)$, then $b\nmid d$.

Prove that MCD is 1 or 3 knowing (a,b) = 1

Prove $m=[a,b]\Longleftrightarrow \left(\frac{m}{a},\frac{m}{b}\right)=1$

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