Number theory: if $(a,b)=1$, show that $(ac,b)=(c,b)$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
5729
If $a^2+b^2+c^2=1$ then prove the following.
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
31173
How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers?
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?