prove if p is a prime having the form 4k+3
121441
$1\cdot3\cdot5 \cdots (p - 2) = (-1)^{m+k+1} \pmod p$, and $2\cdot4\cdot6\cdots(p - 1) = ( -1)^{m +k} \pmod p$.
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
127816
Number theory proof mod p
73515
Primes Number Theory
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
77969
Question about proof for $S_4 \cong V_4 \rtimes S_3$
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
71788
Prove existence of multiplicative inverse modulo p when p is prime
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 $n=3^m$.
116585
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer