List questions from gcd-and-lcm

Published on 16 Mar 2026 - 21:01

146

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How to prove a claim about LCM?

Published on 17 Mar 2026 - 1:04

829

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If c = gcd(a, b), prove that gcd( a/c , b/c ) = 1

Published on 25 Mar 2026 - 1:26

56

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Proof that the GCD of $x^2+x+6$ and $x^2+x+4$ is 2

Published on 22 Mar 2026 - 23:32

47

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Theorem on greatest common divisor

Published on 25 Mar 2026 - 1:33

284

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Finding equivalence classes of gcd

Published on 17 Mar 2026 - 0:59

267

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Proof writing: Let $d=\gcd(a,b)$ and $m=\operatorname{lcm}(a,b)$. Prove that $dm=|ab|$.

Published on 12 Feb 2018 - 0:31

334

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How can I prove $\gcd(10^{a-1}+10^{a-2}+\cdots+1, 10^{b-1}+10^{b-2}+\cdots+1)=10^{\gcd(a,b)-1}+10^{\gcd(a,b)-2}+\cdots+1$?

Published on 13 Feb 2018 - 7:52

74

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Uniqueness of integers satisfying the Extended Euclidian algorithm

Published on 23 Mar 2026 - 6:10

111

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An Integer Linear Combinaton of Rationals is a Cyclic Group

Published on 17 Mar 2026 - 16:42

178

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Prove that every natural number $n >6$ can be written as a sum $a+b$ where $a, b∈\mathbb N\setminus\{1\}$ and$ \gcd(a, b) = 1$

Published on 14 Feb 2018 - 1:26

44

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Given $b\mid (ac-1)$ show that $(a,b) = 1$

Published on 17 Mar 2026 - 9:50

2.8k

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Greatest common divisor of $X^n-1$ and $X^m-1$

Published on 25 Mar 2026 - 3:21

165

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How to show that for each $n\in\mathbb{N}$, $\gcd(3^{n}+5^{n+1},3^{n+1}+5^{n})=2$ or $ 14$?

Published on 21 Feb 2018 - 10:11

55

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When is the sum of coprime pairs coprime?

Published on 17 Mar 2026 - 7:39

List Question

$\gcd (2016!+1, 2015!+1)$

How to prove a claim about LCM?

If c = gcd(a, b), prove that gcd( a/c , b/c ) = 1

Proof that the GCD of $x^2+x+6$ and $x^2+x+4$ is 2

Theorem on greatest common divisor

Finding equivalence classes of gcd

Proof writing: Let $d=\gcd(a,b)$ and $m=\operatorname{lcm}(a,b)$. Prove that $dm=|ab|$.

How can I prove $\gcd(10^{a-1}+10^{a-2}+\cdots+1, 10^{b-1}+10^{b-2}+\cdots+1)=10^{\gcd(a,b)-1}+10^{\gcd(a,b)-2}+\cdots+1$?

Uniqueness of integers satisfying the Extended Euclidian algorithm

An Integer Linear Combinaton of Rationals is a Cyclic Group

Prove that every natural number $n >6$ can be written as a sum $a+b$ where $a, b∈\mathbb N\setminus\{1\}$ and$ \gcd(a, b) = 1$

Given $b\mid (ac-1)$ show that $(a,b) = 1$

Greatest common divisor of $X^n-1$ and $X^m-1$

How to show that for each $n\in\mathbb{N}$, $\gcd(3^{n}+5^{n+1},3^{n+1}+5^{n})=2$ or $ 14$?

When is the sum of coprime pairs coprime?

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