Prove the gcd is 1 when a sequence is purely periodic
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
141895
Proving that a sequence is monotone
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
33628
Prove that $\sin(\sqrt x)$ not periodic
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
79266
Proving a sequence defined by a recurrence relation converges
45460
Proof verification of a number theory problem involving sequences.
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
57592
Does existence of $\gcd$ implies PID?
145354
What is $\gcd(0,0)$?
23076
Proof of limit of quotient sequence property