Question

How to prove that gcd(m+1, n+1) divides (mn-1)

score 3k · Answer 1 · 2017-01-08 20:26:41

How to prove that gcd(m+1, n+1) divides (mn-1)

Published on 08 Jan 2017 - 20:26

score 86 · Answer 2 · 2017-01-09 17:31:21

For $a,b,m,n \in \mathbb{Z}^+$, does there always exist $x,y \in \mathbb{Z}^+$ with ${\rm gcd}(x,y) = 1$ but ${\rm gcd}(ax+m,by+n) > 1$?

score 1.5k · Answer 3 · 2017-01-09 20:55:39

1.5k

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What is the highest common factor of $n$ and $2n + 1$

Published on 09 Jan 2017 - 20:55

score 83 · Answer 4 · 2017-01-10 03:09:49

83

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$\forall n\in\mathbb{Z}$, find the $\gcd(n^2+1, (n+1)^2+1)$?

Published on 10 Jan 2017 - 3:09

score 548 · Answer 5 · 2017-01-10 04:27:46

548

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If two numbers $a$ and $b$ are coprime, then $ab$ and $a^2+b^2$ are also coprime. Why is this true?

Published on 10 Jan 2017 - 4:27

score 160 · Answer 6 · 2026-02-23 06:36:33

160

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$gcd\left(2^{2^n}+1, 2^{2^m}+1\right)$

Published on 23 Feb 2026 - 6:36

score 48 · Answer 7 · 2017-01-10 18:56:59

48

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How to tackle this question related to gcd.

Published on 10 Jan 2017 - 18:56

score 451 · Answer 8 · 2017-01-11 15:45:13

451

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Finding number of Coprime tuples from $1$ to $N$

Published on 11 Jan 2017 - 15:45

score 1.4k · Answer 9 · 2017-01-11 18:08:46

1.4k

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How is induction used to prove that $\gcd(an, bn) = |n|\gcd(a, b)$

Published on 11 Jan 2017 - 18:08

score 283 · Answer 10 · 2017-01-11 22:19:31

283

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What is the maximum gcd of these variables?

Published on 11 Jan 2017 - 22:19

score 931 · Answer 11 · 2017-01-13 17:41:00

931

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proving that elements of a sequence are pairwise coprime

Published on 13 Jan 2017 - 17:41

score 3.3k · Answer 12 · 2026-03-29 22:28:51

3.3k

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How to find number of steps in Euclidean Algorithm for fibonacci numbers

Published on 29 Mar 2026 - 22:28

score 71 · Answer 13 · 2017-01-14 07:56:17

71

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$\gcd(a, b) = \gcd(a, b-a^n)$ where $n\ge 1$ . Is this statement true?

Published on 14 Jan 2017 - 7:56

score 215 · Answer 14 · 2026-03-27 22:00:36

215

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Are there arbitrarily large sets $S$ of natural integers such that the difference of each pair is their GCD?

Published on 27 Mar 2026 - 22:00

score 448 · Answer 15 · 2017-01-16 14:21:20

448

Views

Maximize $GCD$ of list of digits

Published on 16 Jan 2017 - 14:21

List Question

How to prove that gcd(m+1, n+1) divides (mn-1)

For $a,b,m,n \in \mathbb{Z}^+$, does there always exist $x,y \in \mathbb{Z}^+$ with ${\rm gcd}(x,y) = 1$ but ${\rm gcd}(ax+m,by+n) > 1$?

What is the highest common factor of $n$ and $2n + 1$

$\forall n\in\mathbb{Z}$, find the $\gcd(n^2+1, (n+1)^2+1)$?

If two numbers $a$ and $b$ are coprime, then $ab$ and $a^2+b^2$ are also coprime. Why is this true?

$gcd\left(2^{2^n}+1, 2^{2^m}+1\right)$

How to tackle this question related to gcd.

Finding number of Coprime tuples from $1$ to $N$

How is induction used to prove that $\gcd(an, bn) = |n|\gcd(a, b)$

What is the maximum gcd of these variables?

proving that elements of a sequence are pairwise coprime

How to find number of steps in Euclidean Algorithm for fibonacci numbers

$\gcd(a, b) = \gcd(a, b-a^n)$ where $n\ge 1$ . Is this statement true?

Are there arbitrarily large sets $S$ of natural integers such that the difference of each pair is their GCD?

Maximize $GCD$ of list of digits

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