Show that if $a$ is a divisor of $bc$ and $(a, b) = 1$, then $a$ is a divisor of $c$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
27449
Product of Divisors of some $n$ proof
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$