Let $a$ and $b$ be relatively prime integers. Prove $a^2$ and $b^2$ are prime as well.
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
89329
If a and b are relatively prime and ab is a square, then a and b are squares.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
58114
For which primes p is $p^2 + 2$ also prime?
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
34954
If $11..11$($n$ times 1) is prime, prove that $n$ is also prime
135586
Prove that the preimage of a prime ideal is also prime.