List questions from gcd-and-lcm

Published on 05 Apr 2016 - 17:27

212

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Find the least positive integer $n$ for which $n^5+3$, $(n+1)^5+3$ cease to be coprimes

Published on 05 Apr 2016 - 21:11

5.2k

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Proof that lcm(a,b) = ab/gcd(a,b)

Published on 24 Feb 2026 - 5:32

224

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Greatest common divisor theorem

Published on 07 Apr 2016 - 18:00

583

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Does a finite sum of distinct prime reciprocals always give an irreducible fraction?

Published on 08 Apr 2016 - 14:38

104

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greatest common divisor properties

Published on 08 Apr 2016 - 21:37

3k

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If $k$ and $l$ are positive integers such that $k\mid l$, show that for every positive integer $m$, $1+(k+m)l$ and $1+ml$ are relatively prime.

Published on 12 Apr 2016 - 15:10

672

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Formula for calculating the $α$ and $β$ in $\gcd(a, b) = αa + βb$

Published on 28 Mar 2026 - 9:45

125

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If $a, b \in \mathbb{N}$ are relatively prime, show that, for any $k \in \mathbb{N}$, $a^k$ and $b$ are relatively prime.

Published on 13 Apr 2016 - 3:28

278

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How many numbers $m$ satisfy $1 ≤ m ≤ n$ and $\gcd (m, n) = 1$?

Published on 01 Apr 2026 - 20:03

1.5k

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Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $

Published on 14 Apr 2016 - 14:51

54

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Gcd of a Numbers

Published on 17 Apr 2016 - 6:04

989

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how to calculate double sum of GCD(i,j)?

Published on 20 Apr 2016 - 7:38

54

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$\sum_{1 \leq i,j \leq n, i|n, j|n} gcd(i,j)$

Published on 21 Apr 2016 - 8:01

121

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If $a\mid b^2$ and $\gcd(a,b) = 1$, how can I prove that $a\mid b$?

Published on 21 Apr 2016 - 11:14

List Question

Euclidean evaluation

Find the least positive integer $n$ for which $n^5+3$, $(n+1)^5+3$ cease to be coprimes

Proof that lcm(a,b) = ab/gcd(a,b)

Greatest common divisor theorem

Does a finite sum of distinct prime reciprocals always give an irreducible fraction?

greatest common divisor properties

If $k$ and $l$ are positive integers such that $k\mid l$, show that for every positive integer $m$, $1+(k+m)l$ and $1+ml$ are relatively prime.

Formula for calculating the $α$ and $β$ in $\gcd(a, b) = αa + βb$

If $a, b \in \mathbb{N}$ are relatively prime, show that, for any $k \in \mathbb{N}$, $a^k$ and $b$ are relatively prime.

How many numbers $m$ satisfy $1 ≤ m ≤ n$ and $\gcd (m, n) = 1$?

Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $

Gcd of a Numbers

how to calculate double sum of GCD(i,j)?

$\sum_{1 \leq i,j \leq n, i|n, j|n} gcd(i,j)$

If $a\mid b^2$ and $\gcd(a,b) = 1$, how can I prove that $a\mid b$?

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