Q: How to proof there is $x\in \Bbb Z$ such as $gcd (ax+b,c)=1$ if (a,b)=1
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$