Question

Prove that if $m,n,l \in \Bbb N$ and $\operatorname{lcm}(m+l,m)=\operatorname{lcm}(n+l,n)$, then $m=n$ is the only satisfactory solution.

score 36 · Answer 1 · 2020-05-06 18:30:51

Prove that if $m,n,l \in \Bbb N$ and $\operatorname{lcm}(m+l,m)=\operatorname{lcm}(n+l,n)$, then $m=n$ is the only satisfactory solution.

score 160 · Answer 2 · 2020-05-08 13:46:30

160

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I want to gain intuition for least common multiple problems through a specific word problem involving cycle synchronization

Published on 08 May 2020 - 13:46

score 74 · Answer 3 · 2020-05-10 00:45:59

74

Views

How do you find the lcm given the gcd and the number of ordered quadrupules

Published on 10 May 2020 - 0:45

score 127 · Answer 4 · 2020-05-10 19:26:52

127

Views

Prove gcd equality

Published on 10 May 2020 - 19:26

score 117 · Answer 5 · 2020-05-11 14:16:57

117

Views

How can we prove that $\gcd((n^4) + (n+1)^4 , (n+1)^4 + (n+2)^4) = 1$?

Published on 11 May 2020 - 14:16

score 49 · Answer 6 · 2020-05-13 23:08:55

49

Views

gcd(a,b) explanation using the set $\{ax+by : x,y \in \mathbb{Z}\}$

Published on 13 May 2020 - 23:08

score 65 · Answer 7 · 2026-03-26 14:31:53

65

Views

Applying Euclidean Algorithm to find nth value

Published on 26 Mar 2026 - 14:31

score 219 · Answer 8 · 2026-03-25 14:27:00

219

Views

Use the Euclidean algorithm to find the GCD of $1 + 28i$ and $4 + 7i$

Published on 25 Mar 2026 - 14:27

score 76 · Answer 9 · 2020-05-15 09:32:53

76

Views

{$a_n$} $\in N$ .if $(a_m,a_n)=(m,n)$ when $m \ne n$,prove that $a_n=n $ for all $n$

Published on 15 May 2020 - 9:32

score 558 · Answer 10 · 2020-05-20 06:17:07

558

Views

Prove that eventually the numbers will stop changing.

Published on 20 May 2020 - 6:17

score 60 · Answer 11 · 2020-05-21 08:02:17

60

Views

how to extend $ab=gcd(a,b)\cdot lcm(a,b)$ for $n$ integers

Published on 21 May 2020 - 8:02

score 122 · Answer 12 · 2020-05-21 15:50:35

122

Views

Is the group of units of a ring an additive group?

Published on 21 May 2020 - 15:50

score 274 · Answer 13 · 2020-05-23 00:25:46

274

Views

Prove or disprove $\frac{(x+n)!}{(x!)\text{lcm}(x+1, \dots, x+n)} < (n-1)!$

Published on 23 May 2020 - 0:25

score 679 · Answer 14 · 2020-05-23 04:53:50

679

Views

Express $ \operatorname{gcd}\left(5^{m}+7^{m}, 5^{n}+7^{n}\right) $ in terms of $m$ and $n$

Published on 23 May 2020 - 4:53

score 93 · Answer 15 · 2020-05-23 06:36:06

93

Views

Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?

Published on 23 May 2020 - 6:36

List Question

Prove that if $m,n,l \in \Bbb N$ and $\operatorname{lcm}(m+l,m)=\operatorname{lcm}(n+l,n)$, then $m=n$ is the only satisfactory solution.

I want to gain intuition for least common multiple problems through a specific word problem involving cycle synchronization

How do you find the lcm given the gcd and the number of ordered quadrupules

Prove gcd equality

How can we prove that $\gcd((n^4) + (n+1)^4 , (n+1)^4 + (n+2)^4) = 1$?

gcd(a,b) explanation using the set $\{ax+by : x,y \in \mathbb{Z}\}$

Applying Euclidean Algorithm to find nth value

Use the Euclidean algorithm to find the GCD of $1 + 28i$ and $4 + 7i$

{$a_n$} $\in N$ .if $(a_m,a_n)=(m,n)$ when $m \ne n$,prove that $a_n=n $ for all $n$

Prove that eventually the numbers will stop changing.

how to extend $ab=gcd(a,b)\cdot lcm(a,b)$ for $n$ integers

Is the group of units of a ring an additive group?

Prove or disprove $\frac{(x+n)!}{(x!)\text{lcm}(x+1, \dots, x+n)} < (n-1)!$

Express $ \operatorname{gcd}\left(5^{m}+7^{m}, 5^{n}+7^{n}\right) $ in terms of $m$ and $n$

Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?

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