Proof that if that if m is odd then gcd(5,2^m-1)=1
51858
Showing $\gcd(2^m-1,2^n+1)=1$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
95036
For any integer $a$, $\gcd(11a+5,2a+1)=1$.
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
85272
$3x + 1$ is even iff $5x-2$ is odd
63769
Group theory proof of Euler's theorem ($a^{\phi(m)} \equiv 1\mbox{ }(\mbox{mod }m)$ if $\gcd(a,m)=1$)
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$