Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)