List questions from gcd-and-lcm

Published on 23 Feb 2026 - 6:58

72

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If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

Published on 07 Dec 2018 - 2:32

36

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If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

Published on 23 Feb 2026 - 7:01

51

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Which is the gcd of 2 numbers which are multiplied and the result is 600000?

Published on 11 Dec 2018 - 18:32

116

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Determine the number of positive integers $a$ such that $a\mid 9!$ and gcd $(a, 3600)=180$.

Published on 26 Mar 2026 - 4:53

1.3k

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Proving fraction is irreducible

Published on 25 Mar 2026 - 23:10

5.1k

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Prove $\gcd(n,n+2)=1$ if $n$ is odd and $2$ if $n$ is even

Published on 14 Dec 2018 - 3:02

93

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On randomly permuting digits in a large random number

Published on 25 Mar 2026 - 22:09

48

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Is this proof acceptable?

Published on 23 Feb 2026 - 6:52

67

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If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Published on 23 Feb 2026 - 7:02

227

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Why $\mathbb{C}(f(t),g(t))=\mathbb{C}(t)$ implies that $\gcd(f(t)-a,g(t)-b)=t-c$, for some $a,b,c \in \mathbb{C}$?

Published on 15 Dec 2018 - 22:08

131

Views

Show that $\text{gcd}(a,b,c) = 1$ implies existence of $k$ such that $\text{gcd}(a, b+kc)=1$

Published on 19 Dec 2018 - 10:28

47

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Divide money and things equally between room mates

Published on 25 Mar 2026 - 1:23

107

Views

Is it true that $\gcd(s(p^k), D(p^k)) = 1$?

Published on 25 Mar 2026 - 10:55

1.2k

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Relation between GCD and LCM

Published on 23 Feb 2026 - 6:52

List Question

Product of gcd and lcm for multivariate polynomials

If $m, n>0$ and $\gcd(m, n) =d$, then $\gcd(a^m-1, a^n-1) =a^d-1$.

If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

Which is the gcd of 2 numbers which are multiplied and the result is 600000?

Determine the number of positive integers $a$ such that $a\mid 9!$ and gcd $(a, 3600)=180$.

Proving fraction is irreducible

Prove $\gcd(n,n+2)=1$ if $n$ is odd and $2$ if $n$ is even

On randomly permuting digits in a large random number

Is this proof acceptable?

If $1\le a_1<\cdots<a_n\le 2n$ satisfy $\operatorname{lcm}(a_i,a_j)>2n$ for $i\ne j$, is $a_i>\frac{2n}{3}$ for all $i$?

Why $\mathbb{C}(f(t),g(t))=\mathbb{C}(t)$ implies that $\gcd(f(t)-a,g(t)-b)=t-c$, for some $a,b,c \in \mathbb{C}$?

Show that $\text{gcd}(a,b,c) = 1$ implies existence of $k$ such that $\text{gcd}(a, b+kc)=1$

Divide money and things equally between room mates

Is it true that $\gcd(s(p^k), D(p^k)) = 1$?

Relation between GCD and LCM

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