Proof about prime factors: every prime factor of $4n^2+1$ is congruent to $1 \pmod 4$.
34097
Is it possible that $n^2+1$ has some divisor of the form $4k+3$?
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
130842
Prime factors + number of Divisors
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
19761
Show for prime numbers of the form $p=4n+1$,  $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.
16621
Help understand the proof of infinitely many primes of the form $4n+3$
75733
Divisibility of prime numbers
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
23544
Complete induction proof that every $n > 1$ can be written as a product of primes
78259
Prime factorization