Question

Finding a multiple of a given number which can be expressed as 1+2+...+x

score 75 · Answer 1 · 2020-04-18 12:10:54

75

Views

Finding a multiple of a given number which can be expressed as 1+2+...+x

Published on 18 Apr 2020 - 12:10

score 1.4k · Answer 2 · 2026-03-26 11:00:19

1.4k

Views

Finding GCD of powers and factorial numbers

Published on 26 Mar 2026 - 11:00

score 1k · Answer 3 · 2020-04-21 03:59:51

1k

Views

Justifying expansion: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$

Published on 21 Apr 2020 - 3:59

score 39 · Answer 4 · 2020-04-22 03:55:25

39

Views

Prove gcd(a,b) = gcd(a+c,b) given b|c

Published on 22 Apr 2020 - 3:55

score 72 · Answer 5 · 2020-04-22 13:31:17

72

Views

Let $\gcd(x_1,n)=d_1, \gcd(x_2,n)=d_2$ where $1\le x_1,x_2\le n-1$. Find $\gcd(x_1,x_2)$.

Published on 22 Apr 2020 - 13:31

score 73 · Answer 6 · 2020-04-24 00:17:45

73

Views

Let $a,b\in\Bbb{N}$ such that $\gcd(a,b)=1$ and $n,r\in\Bbb{N}^*$. If $ab=n^r$ then there exists $k,l\in\Bbb{N}$ such that $a=k^r$ and $b=l^r$.

Published on 24 Apr 2020 - 0:17

score 83 · Answer 7 · 2020-04-24 20:31:43

83

Views

If $(a,b) = 1$, then $(n, ab) = 1 \iff (n,a) = 1 = (n,b)$. How to prove it?

Published on 24 Apr 2020 - 20:31

score 267 · Answer 8 · 2026-03-25 10:59:03

267

Views

If an arithmetic function $f$ satisfies $f(mn) \leq f(m)f(n)$ (whenever $\gcd(m,n)=1$), is $f$ weakly multiplicative or submultiplicative?

Published on 25 Mar 2026 - 10:59

score 303 · Answer 9 · 2020-04-25 12:24:05

303

Views

Problem from the 1998 Hungarian Math Olympiad

Published on 25 Apr 2020 - 12:24

score 468 · Answer 10 · 2020-04-27 17:07:57

468

Views

how to prove lcm divides any common multiple from definition of lcm(a,b) = (a*b)/gcd(a,b)

Published on 27 Apr 2020 - 17:07

score 54 · Answer 11 · 2020-04-29 05:08:50

54

Views

Prove $\,a\mid A,\, b\mid B\,\Rightarrow\, {\rm lcm}(a,b)\mid {\rm lcm}(A,B)$

Published on 29 Apr 2020 - 5:08

score 508 · Answer 12 · 2020-04-29 19:01:46

508

Views

If $X=\text{GCD}(x_1,x_2,\dots,x_n)$, then find $E(X)$

Published on 29 Apr 2020 - 19:01

score 91 · Answer 13 · 2020-05-01 21:33:39

91

Views

Algebra question on transformation of an n-tuple to $a = (a_1, \dots , a_n)$ to $(1, 0, \dots ,0)$

Published on 01 May 2020 - 21:33

score 62 · Answer 14 · 2026-03-26 09:38:13

62

Views

GCD / proof by induction / well founded order

Published on 26 Mar 2026 - 9:38

score 564 · Answer 15 · 2026-03-26 11:01:18

564

Views

If $f(x)$ is a common factor of $g(x)$ and $h(x)$ find $f(x)$

Published on 26 Mar 2026 - 11:01

List Question

Finding a multiple of a given number which can be expressed as 1+2+...+x

Finding GCD of powers and factorial numbers

Justifying expansion: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$

Prove gcd(a,b) = gcd(a+c,b) given b|c

Let $\gcd(x_1,n)=d_1, \gcd(x_2,n)=d_2$ where $1\le x_1,x_2\le n-1$. Find $\gcd(x_1,x_2)$.

Let $a,b\in\Bbb{N}$ such that $\gcd(a,b)=1$ and $n,r\in\Bbb{N}^*$. If $ab=n^r$ then there exists $k,l\in\Bbb{N}$ such that $a=k^r$ and $b=l^r$.

If $(a,b) = 1$, then $(n, ab) = 1 \iff (n,a) = 1 = (n,b)$. How to prove it?

If an arithmetic function $f$ satisfies $f(mn) \leq f(m)f(n)$ (whenever $\gcd(m,n)=1$), is $f$ weakly multiplicative or submultiplicative?

Problem from the 1998 Hungarian Math Olympiad

how to prove lcm divides any common multiple from definition of lcm(a,b) = (a*b)/gcd(a,b)

Prove $\,a\mid A,\, b\mid B\,\Rightarrow\, {\rm lcm}(a,b)\mid {\rm lcm}(A,B)$

If $X=\text{GCD}(x_1,x_2,\dots,x_n)$, then find $E(X)$

Algebra question on transformation of an n-tuple to $a = (a_1, \dots , a_n)$ to $(1, 0, \dots ,0)$

GCD / proof by induction / well founded order

If $f(x)$ is a common factor of $g(x)$ and $h(x)$ find $f(x)$

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