If a prime (of the form $4k+3$) divides the sum of two squares, then it divides each of the two numbers
131731
Primes that can't be written as sum of two squares. Mod
72666
Prime Numbers And Perfect Squares
120282
Sum of two co-prime integers
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
73515
Primes Number Theory
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
21898
Find all primes $p$ such that $ p^3-4p+9 $ is a perfect square.
80907
Primes dividing a polynomial
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
155452
Prime factorization of square numbers
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
19979
Why does $p^2+8$ prime imply $p^3+4$ prime