What is different $(a_0, a_1, ..., a_d) = (1)$ and $\gcd(a_0, a_1, ..., a_d) = 1$ in arbitrary UFD?
57592
Does existence of $\gcd$ implies PID?
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
103578
Affine cipher : Why it is required to have GCD(a, m) equals to 1
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
135086
GCD of two numbers divided by their greatest common divisor is 1
94722
GCD expressed with irreducible elements in a unique factorization domain
51538
Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
28987
One-dimensional [Noetherian] UFD is a PID
4425
Why are integer GCDs positive? [unit normalization of GCDs]
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
63547
Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?