Using divisibility and greatest common divisor for a proof
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
27250
Greatest common divisor of two relatively primes
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
3632
Basic number theory proofs
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
84501
Proof involving Cyclic group, generator and GCD