Question

Let $n$ and $k$ be positive integers. Show that $\gcd(n, nk \pm 1) = 1$

score 347 · Answer 1 · 2021-03-14 10:20:04

347

Views

Let $n$ and $k$ be positive integers. Show that $\gcd(n, nk \pm 1) = 1$

Published on 14 Mar 2021 - 10:20

score 109 · Answer 2 · 2021-03-14 15:17:02

109

Views

Let $m$ and $n$ be integers such that $\gcd (m, n) = 1$. Show that $\gcd (m + n, m - n) = 1$ or $2$

Published on 14 Mar 2021 - 15:17

score 90 · Answer 3 · 2026-03-29 14:19:52

90

Views

Given that and are positive integers with $\mid$, how would one prove that $\gcd(, ) = $?

Published on 29 Mar 2026 - 14:19

score 100 · Answer 4 · 2026-03-30 10:54:36

100

Views

Intuitive proof for $(a, b) = (a', b')$.

Published on 30 Mar 2026 - 10:54

score 63 · Answer 5 · 2021-03-19 12:59:52

63

Views

Need help understanding this tricky LCM problem.

Published on 19 Mar 2021 - 12:59

score 46 · Answer 6 · 2021-03-20 18:33:10

Prove that $\gcd(a^{2^m}+1,a^{2^n}+1)=\begin{cases} 1,& \text{ if } a\ \text{is even;} \\ 2 & \text{ if } a\ \text{is odd.} \end{cases}$.

score 172 · Answer 7 · 2021-03-22 15:21:42

172

Views

Find numbers from GCD and LCM

Published on 22 Mar 2021 - 15:21

score 261 · Answer 8 · 2026-03-29 15:54:49

261

Views

Find the GCD of a polynomial using the extended Euclidean algorithm and express it in the form $a(x)f(x)+b(x)g(x)$

Published on 29 Mar 2026 - 15:54

score 82 · Answer 9 · 2021-03-24 10:13:59

82

Views

Formulas for lcm of three integers

Published on 24 Mar 2021 - 10:13

score 40 · Answer 10 · 2021-03-26 23:55:34

How can I prove that for modular multiplicative inverses that if $∃ $[$b$]$ ∈ℤ_n$ such that [$a$] * [$b$] = [$1$], then gcd($a,n$) =$1$?

score 147 · Answer 11 · 2021-03-30 04:53:46

147

Views

How to find $\gcd(n+1, n^2+7)$?

Published on 30 Mar 2021 - 4:53

score 165 · Answer 12 · 2021-03-30 11:18:54

165

Views

Prove that $\gcd(5x+2y,2x+y)=1$ if $\gcd(x,y)=1$

Published on 30 Mar 2021 - 11:18

score 74 · Answer 13 · 2021-04-04 20:24:53

74

Views

$a_1<a_2<a_3<a_4$ such that $\sum_{i=1}^4\frac{1}{a_i}=\frac{11}{6}$

Published on 04 Apr 2021 - 20:24

score 101 · Answer 14 · 2021-04-08 23:33:12

101

Views

Irreducible polynomial written as $ap + bq$

Published on 08 Apr 2021 - 23:33

score 411 · Answer 15 · 2021-04-10 14:24:10

411

Views

a number plus by gcd

Published on 10 Apr 2021 - 14:24

List Question

Let $n$ and $k$ be positive integers. Show that $\gcd(n, nk \pm 1) = 1$

Let $m$ and $n$ be integers such that $\gcd (m, n) = 1$. Show that $\gcd (m + n, m - n) = 1$ or $2$

Given that and are positive integers with $\mid$, how would one prove that $\gcd(, ) = $?

Intuitive proof for $(a, b) = (a', b')$.

Need help understanding this tricky LCM problem.

Prove that $\gcd(a^{2^m}+1,a^{2^n}+1)=\begin{cases} 1,& \text{ if } a\ \text{is even;} \\ 2 & \text{ if } a\ \text{is odd.} \end{cases}$.

Find numbers from GCD and LCM

Find the GCD of a polynomial using the extended Euclidean algorithm and express it in the form $a(x)f(x)+b(x)g(x)$

Formulas for lcm of three integers

How can I prove that for modular multiplicative inverses that if $∃ $[$b$]$ ∈ℤ_n$ such that [$a$] * [$b$] = [$1$], then gcd($a,n$) =$1$?

How to find $\gcd(n+1, n^2+7)$?

Prove that $\gcd(5x+2y,2x+y)=1$ if $\gcd(x,y)=1$

$a_1<a_2<a_3<a_4$ such that $\sum_{i=1}^4\frac{1}{a_i}=\frac{11}{6}$

Irreducible polynomial written as $ap + bq$

a number plus by gcd

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