If $x|yz$ and $\gcd(x, y)$ = 1 then $x|z, x, y, z \in \mathbb{Z}$
109325
Euclid Lemma proof reasoning
29608
If GCD $(a_1,\ldots, a_n)=1$ then there's a matrix in $SL_n(\mathbb{Z})$ with first row $(a_1,\ldots, a_n)$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
59856
Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$