$a_k$ is a countable sequence of positive numbers st. $\gcd(a_1,a_2,...)=1$, show exists a finite subsequence $a_{i_1},a_{i_2},...,a_{i_n}$ with gcd 1

score 36 · Answer 7 · 2016-01-18 02:02:11

36

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Prove $2^a+1\mid 2^{ab}+1$ if $2\nmid b$, $a,b\in\mathbb{Z}^{+}$

Published on 18 Jan 2016 - 2:02

score 183 · Answer 8 · 2016-01-21 17:45:42

183

Views

If $\gcd (a,b) = 1$ then $\gcd (a^n,b^k) = 1$

Published on 21 Jan 2016 - 17:45

score 5k · Answer 9 · 2026-03-28 04:23:21

5k

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Finding $d=\gcd(a,b)$; finding integers $m$ and $n$: $d=ma+nb$

Published on 28 Mar 2026 - 4:23

score 91 · Answer 10 · 2016-01-23 23:04:17

91

Views

There exists integers such that 200s + 567t = 1. Find s.

Published on 23 Jan 2016 - 23:04

score 1.1k · Answer 11 · 2016-01-25 11:56:15

1.1k

Views

Prove that greatest common divisor of two numbers multiplied with itself divides the product of those numbers

Published on 25 Jan 2016 - 11:56

score 104 · Answer 12 · 2016-01-25 20:15:43

104

Views

Calculate the sum under gcd

Published on 25 Jan 2016 - 20:15

score 63 · Answer 13 · 2016-02-02 00:27:40

63

Views

Let $n>0$ and $m>0$ be integers, and let $c = \gcd(n,m).$ Show that $\gcd\left(\frac{n}{c},\frac{m}{c}\right) = 1.$

Published on 02 Feb 2016 - 0:27

score 296 · Answer 14 · 2016-02-03 03:38:48

296

Views

If ad = bc, (a, b) = 1, (c, d) = 1, and a, b, c, and d are all positive, show a = c and b = d.

Published on 03 Feb 2016 - 3:38

score 76 · Answer 15 · 2026-03-28 07:59:32

76

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Let $n$ be positive and $a > 1$. Show that $\gcd(\frac{a^n - 1}{a-1}, a-1) = \gcd(a-1, n)$

Published on 28 Mar 2026 - 7:59

List Question

Greatest Common Divisor of a+b,a-b

Show that if the gcd of a set of non-negative integers $n_1,n_2,...,n_k$ is 1, then there exists $c_1,...,c_k\in\Bbb Z$ st. $\sum_{i=1}^k c_in_i=1$

Solve for $A,B$: $\mathrm{LCM}(A,B)=168$, $\mathrm{HCF(A,B)}=12$

Given a sequence $a_1,a_2,\ldots ,a_n$, if $\gcd(a_1,a_2,\ldots ,a_n) = 1$, then there exists one pair $a_i,a_j$ st. $\gcd(a_i,a_j)=1$.

Suppose $d$ is a common divisor of two numbers $a_0$ and $a_1$, can $d$ be written as a linear combination of $a_0$,$a_1$ with integer coefficients?

$a_k$ is a countable sequence of positive numbers st. $\gcd(a_1,a_2,...)=1$, show exists a finite subsequence $a_{i_1},a_{i_2},...,a_{i_n}$ with gcd 1

Prove $2^a+1\mid 2^{ab}+1$ if $2\nmid b$, $a,b\in\mathbb{Z}^{+}$

If $\gcd (a,b) = 1$ then $\gcd (a^n,b^k) = 1$

Finding $d=\gcd(a,b)$; finding integers $m$ and $n$: $d=ma+nb$

There exists integers such that 200s + 567t = 1. Find s.

Prove that greatest common divisor of two numbers multiplied with itself divides the product of those numbers

Calculate the sum under gcd

Let $n>0$ and $m>0$ be integers, and let $c = \gcd(n,m).$ Show that $\gcd\left(\frac{n}{c},\frac{m}{c}\right) = 1.$

If ad = bc, (a, b) = 1, (c, d) = 1, and a, b, c, and d are all positive, show a = c and b = d.

Let $n$ be positive and $a > 1$. Show that $\gcd(\frac{a^n - 1}{a-1}, a-1) = \gcd(a-1, n)$

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