Prove that if $p, q$ are relatively prime, then so are $p^n, q^n$.
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
75516
Relatively Prime Numbers and Number of Divisors of n
85006
If $a$ and $b$ are relatively prime, prove that $a + 2b$ and $2a+b$ are also relatively prime or have a gcd of $3$.
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?