Question

Compute $\langle 3, 5\rangle$ in $U_{16}$

score 96 · Answer 1 · 2015-09-20 02:55:22

96

Views

Compute $\langle 3, 5\rangle$ in $U_{16}$

Published on 20 Sep 2015 - 2:55

score 83 · Answer 2 · 2015-09-20 09:09:42

83

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If $(b,n)=1$, $n\mid(ad-bc)$ and $n\mid(a-b)$ then $n\mid (c-d)$.

Published on 20 Sep 2015 - 9:09

score 136 · Answer 3 · 2015-09-20 21:30:59

136

Views

Show a piecewise-defined function is one-to-one

Published on 20 Sep 2015 - 21:30

score 500 · Answer 4 · 2015-09-21 07:15:51

500

Views

If $a | b$, prove that $\gcd(a,b)$=$|a|$.

Published on 21 Sep 2015 - 7:15

score 4k · Answer 5 · 2015-09-21 18:56:53

4k

Views

True or False: $\operatorname{gcd}(a,b) = \operatorname{gcd}(5a+b, 3a+2b)$

Published on 21 Sep 2015 - 18:56

score 106 · Answer 6 · 2015-09-23 02:55:03

Suppose a is a number > 1 with the following property: for all b,c, if a divides bc and a does not divide b, then a divides c. Show a must be prime

score 1.1k · Answer 7 · 2015-09-26 04:28:12

1.1k

Views

$\gcd(0.5,2.5)=1$ or $0.5$?

Published on 26 Sep 2015 - 4:28

score 2.9k · Answer 8 · 2026-04-01 21:57:32

2.9k

Views

Let $H$ be a group. Let $a, b$ be fixed positive integers and $H=\{ax+by\mid x,y\in \Bbb Z\}.$ Show that $d\mathbb Z =H$ where $d=\gcd(a,b)$.

Published on 01 Apr 2026 - 21:57

score 144 · Answer 9 · 2026-03-27 13:46:19

144

Views

is $\Bbb{Q}$ a GCD Domain?

Published on 27 Mar 2026 - 13:46

score 592 · Answer 10 · 2015-09-27 15:10:33

592

Views

Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$

Published on 27 Sep 2015 - 15:10

score 226 · Answer 11 · 2026-02-24 00:49:29

226

Views

How to find upper-bound on the complexity to compute $\text{lcm}(a,b)$ using $\text{lcm}(a,b) = \frac{ab}{\gcd(a,b)}$

Published on 24 Feb 2026 - 0:49

score 68 · Answer 12 · 2015-09-29 02:28:28

68

Views

How to prove: if $a$ is an even integer, $\gcd(a^3 - 1, a + 1) = 1$

Published on 29 Sep 2015 - 2:28

score 612 · Answer 13 · 2015-09-30 15:22:02

Suppose $b,c \in \textbf Z^+$ are relatively prime (i.e., $\gcd(b,c) = 1$), and $a \,|\, (b+c)$. Prove that $\gcd(a,b) = 1$ and $\gcd(a,c) = 1$

score 149 · Answer 14 · 2015-10-01 10:51:04

149

Views

Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$

Published on 01 Oct 2015 - 10:51

score 1k · Answer 15 · 2026-03-27 23:30:56

1k

Views

Finding GCD of two polynomials over a ring

Published on 27 Mar 2026 - 23:30

List Question

Compute $\langle 3, 5\rangle$ in $U_{16}$

If $(b,n)=1$, $n\mid(ad-bc)$ and $n\mid(a-b)$ then $n\mid (c-d)$.

Show a piecewise-defined function is one-to-one

If $a | b$, prove that $\gcd(a,b)$=$|a|$.

True or False: $\operatorname{gcd}(a,b) = \operatorname{gcd}(5a+b, 3a+2b)$

Suppose a is a number > 1 with the following property: for all b,c, if a divides bc and a does not divide b, then a divides c. Show a must be prime

$\gcd(0.5,2.5)=1$ or $0.5$?

Let $H$ be a group. Let $a, b$ be fixed positive integers and $H=\{ax+by\mid x,y\in \Bbb Z\}.$ Show that $d\mathbb Z =H$ where $d=\gcd(a,b)$.

is $\Bbb{Q}$ a GCD Domain?

Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$

How to find upper-bound on the complexity to compute $\text{lcm}(a,b)$ using $\text{lcm}(a,b) = \frac{ab}{\gcd(a,b)}$

How to prove: if $a$ is an even integer, $\gcd(a^3 - 1, a + 1) = 1$

Suppose $b,c \in \textbf Z^+$ are relatively prime (i.e., $\gcd(b,c) = 1$), and $a \,|\, (b+c)$. Prove that $\gcd(a,b) = 1$ and $\gcd(a,c) = 1$

Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$

Finding GCD of two polynomials over a ring

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