Question

$a,b\in\mathbb Z^+$, and the equations given are $a-b=120$, and $\operatorname{lcm}(a,b)=105\gcd(a,b)$. What is $a$?

score 74 · Answer 1 · 2020-09-14 18:15:29

74

Views

$a,b\in\mathbb Z^+$, and the equations given are $a-b=120$, and $\operatorname{lcm}(a,b)=105\gcd(a,b)$. What is $a$?

Published on 14 Sep 2020 - 18:15

score 92 · Answer 2 · 2020-09-16 11:47:08

92

Views

Find the unknowns from LCM HCF relation.

Published on 16 Sep 2020 - 11:47

score 185 · Answer 3 · 2020-09-16 11:57:25

185

Views

$\gcd(a_1,...,a_n)=\gcd(\gcd(a_1,...,a_{n-1}),a_n)$

Published on 16 Sep 2020 - 11:57

score 332 · Answer 4 · 2020-09-20 10:09:47

332

Views

Prove that $g(x,y) = \gcd(x,y)$

Published on 20 Sep 2020 - 10:09

score 605 · Answer 5 · 2020-09-22 01:40:27

605

Views

Find all positive integer values $(x, y, n)$ such that $x^n+1=y^{n+1}$ and $gcd(x, n+1)=1$

Published on 22 Sep 2020 - 1:40

score 50 · Answer 6 · 2020-09-22 02:42:32

50

Views

Prove that if $a|bc$ and $\gcd(a,b)|c$ , then $a|c^2$

Published on 22 Sep 2020 - 2:42

score 125 · Answer 7 · 2020-09-23 21:36:52

125

Views

Prove that if both $x$ and $y$ are odd, then $\gcd(x, y)=\gcd\left(\frac{x-y}{2}, y\right)$

Published on 23 Sep 2020 - 21:36

score 245 · Answer 8 · 2026-03-29 07:28:43

245

Views

Prove consecutive Fibonacci numbers are coprime

Published on 29 Mar 2026 - 7:28

score 86 · Answer 9 · 2020-09-24 10:44:05

86

Views

Finding the gcd of polynomials $p,q$ and writing $\gcd(p,q)=d_1(x)p+d_2(x)q$

Published on 24 Sep 2020 - 10:44

score 129 · Answer 10 · 2020-09-24 15:44:43

129

Views

showing all gcd $(n^3-n, 2n^2-1)$

Published on 24 Sep 2020 - 15:44

score 440 · Answer 11 · 2020-09-24 17:30:48

440

Views

Prove that: If $a,b,c \in \mathbb{N},$ then lcm (ca,cb) = c · lcm(a,b)

Published on 24 Sep 2020 - 17:30

score 93 · Answer 12 · 2020-09-25 06:49:26

93

Views

Prove that the gcd of ( 8n+19 , 3n+7 ) =1

Published on 25 Sep 2020 - 6:49

score 191 · Answer 13 · 2020-09-26 06:59:45

191

Views

to find the smallest value of n

Published on 26 Sep 2020 - 6:59

score 67 · Answer 14 · 2026-03-31 11:58:17

67

Views

Please find error in proof If c|a and c|b then $cgcd(a/c, b/c)=gcd(a, b)$

Published on 31 Mar 2026 - 11:58

score 337 · Answer 15 · 2026-03-29 07:22:25

337

Views

How do I know how many iterations an arbitrary extended gcd algorithm would take?

Published on 29 Mar 2026 - 7:22

List Question

$a,b\in\mathbb Z^+$, and the equations given are $a-b=120$, and $\operatorname{lcm}(a,b)=105\gcd(a,b)$. What is $a$?

Find the unknowns from LCM HCF relation.

$\gcd(a_1,...,a_n)=\gcd(\gcd(a_1,...,a_{n-1}),a_n)$

Prove that $g(x,y) = \gcd(x,y)$

Find all positive integer values $(x, y, n)$ such that $x^n+1=y^{n+1}$ and $gcd(x, n+1)=1$

Prove that if $a|bc$ and $\gcd(a,b)|c$ , then $a|c^2$

Prove that if both $x$ and $y$ are odd, then $\gcd(x, y)=\gcd\left(\frac{x-y}{2}, y\right)$

Prove consecutive Fibonacci numbers are coprime

Finding the gcd of polynomials $p,q$ and writing $\gcd(p,q)=d_1(x)p+d_2(x)q$

showing all gcd $(n^3-n, 2n^2-1)$

Prove that: If $a,b,c \in \mathbb{N},$ then lcm (ca,cb) = c · lcm(a,b)

Prove that the gcd of ( 8n+19 , 3n+7 ) =1

to find the smallest value of n

Please find error in proof If c|a and c|b then $cgcd(a/c, b/c)=gcd(a, b)$

How do I know how many iterations an arbitrary extended gcd algorithm would take?

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