Proof that if $\gcd(a,p^2)=p$ and $\gcd(b,p^3)=p^2$ then $(ab,p^4)=p^3$
70628
Prove p-adic valuation is completely additive for prime p
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
152878
calculate the gcd of $a+b$ and $p^4$
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$