If $p$ is prime and $a \not \equiv 0 \pmod p$, then $a$ and $p$ are relatively prime (in the abstract setting)
137840
Herstein Topics in Algebra, $\pi \mid a$ or $(\pi,a) = 1$
17233
are two consecutive numbers relatively prime?
89329
If a and b are relatively prime and ab is a square, then a and b are squares.
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
53525
Infiniteness of non-twin primes.
46383
If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
133617
Relatively prime property verification
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
27250
Greatest common divisor of two relatively primes
89066
Find all integers less than $m$ that are relatively prime to it
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
78342
When is $\phi(n)$ a prime number?
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime