Suppose that gcd($a,p$) = gcd($b,p$) = 1, and neither of the congruences $x^2 ...
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
158025
Intuition of why $\gcd(a,b) = \gcd(b, a \pmod b)$?
1197
Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$