Question

For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?

score 157 · Answer 1 · 2026-03-26 12:37:49

157

Views

For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?

Published on 26 Mar 2026 - 12:37

score 942 · Answer 2 · 2016-09-19 21:50:12

942

Views

If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$

Published on 19 Sep 2016 - 21:50

score 46 · Answer 3 · 2026-03-26 14:34:36

46

Views

Extended $\gcd$ of $f(x)$ and $g(x)$

Published on 26 Mar 2026 - 14:34

score 117 · Answer 4 · 2016-09-20 20:15:00

117

Views

If $a$ and $b$ are odd then $2(a,b)=(a+b,a−b)$.

Published on 20 Sep 2016 - 20:15

score 48 · Answer 5 · 2016-09-21 11:34:54

48

Views

If $\gcd(n,q_1)=1$ then show that $\gcd(n+tq_1,q)=1$ for some $t$

Published on 21 Sep 2016 - 11:34

score 181 · Answer 6 · 2026-03-27 15:18:13

181

Views

Donald Knuth Concrete Mathematics Page 94 (Topic Integer Functions Floor Ceiling Sums)

Published on 27 Mar 2026 - 15:18

score 2.8k · Answer 7 · 2016-09-25 15:19:51

2.8k

Views

Proof that if $n>0$, $a=nm$, $b=np$, $c=nq$, then $\gcd(m,p,q)=1$ iff $n=\gcd(a,b,c)$

Published on 25 Sep 2016 - 15:19

score 2.6k · Answer 8 · 2016-09-25 20:01:12

2.6k

Views

a divides bc if and only if

Published on 25 Sep 2016 - 20:01

score 108 · Answer 9 · 2016-09-28 20:33:40

108

Views

Linear combinations and GCD

Published on 28 Sep 2016 - 20:33

score 204 · Answer 10 · 2026-03-26 16:03:50

204

Views

Euclid's lemma, mod, gcd proof

Published on 26 Mar 2026 - 16:03

score 58 · Answer 11 · 2016-09-29 08:51:01

58

Views

Greatest common denominator: $x\mid a$ and $x\mid b$ iff $x\mid\gcd(a,b)$

Published on 29 Sep 2016 - 8:51

score 2.1k · Answer 12 · 2016-09-29 18:39:38

2.1k

Views

Find the smallest number that when multiplied with a decimal will give a whole number

Published on 29 Sep 2016 - 18:39

score 309 · Answer 13 · 2016-10-02 19:16:43

309

Views

If d divides N, and gcd(k,d)=1, show that there exists an integer m such that gcd( k+md, N)=1.

Published on 02 Oct 2016 - 19:16

score 65 · Answer 14 · 2016-10-05 05:01:01

65

Views

Suppose a in an integer, and p is prime. Prove that if $gcd(a,p)>1$, then $p$ divides $a$

Published on 05 Oct 2016 - 5:01

score 1k · Answer 15 · 2016-10-05 07:51:12

1k

Views

If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$

Published on 05 Oct 2016 - 7:51

List Question

For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?

If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$

Extended $\gcd$ of $f(x)$ and $g(x)$

If $a$ and $b$ are odd then $2(a,b)=(a+b,a−b)$.

If $\gcd(n,q_1)=1$ then show that $\gcd(n+tq_1,q)=1$ for some $t$

Donald Knuth Concrete Mathematics Page 94 (Topic Integer Functions Floor Ceiling Sums)

Proof that if $n>0$, $a=nm$, $b=np$, $c=nq$, then $\gcd(m,p,q)=1$ iff $n=\gcd(a,b,c)$

a divides bc if and only if

Linear combinations and GCD

Euclid's lemma, mod, gcd proof

Greatest common denominator: $x\mid a$ and $x\mid b$ iff $x\mid\gcd(a,b)$

Find the smallest number that when multiplied with a decimal will give a whole number

If d divides N, and gcd(k,d)=1, show that there exists an integer m such that gcd( k+md, N)=1.

Suppose a in an integer, and p is prime. Prove that if $gcd(a,p)>1$, then $p$ divides $a$

If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$

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