Disprove that for all integers $a,b$ that if $d=gcd(a,b)$ then $d=gcd(a^2,b)$ or $d=gcd(a,b^2)$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
135011
Number of pairs $(A,B)$ with $\gcd(A,B)=B, A \ne B^2$ with $A,B \le n$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$