If $a$ and $b$ are relatively prime, are $a^n$ and $b^n$ too?
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
75516
Relatively Prime Numbers and Number of Divisors of n
53475
Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
2522
Why is $a^n - b^n$ divisible by $a-b$?
76826
Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
27069
sum of all positive integers less than $n$ and relatively prime to $n$
89329
If a and b are relatively prime and ab is a square, then a and b are squares.
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
127293
Prove that $(a-b) \mid (a^n-b^n)$
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?