$-1$ isn't a quadratic residue $\pmod{p}, p=4k+3$.
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
38876
$r! \equiv (−1)^k \pmod p$
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
148671
Trying to factor $x^4-3$ over $\Bbb{F}_p$ with $p\equiv 3\mod{4}$
115758
Remainder of division when $p$ is not prime
63493
Why 4 is not a primitive root modulo p for any prime p?
121441
$1\cdot3\cdot5 \cdots (p - 2) = (-1)^{m+k+1} \pmod p$, and $2\cdot4\cdot6\cdots(p - 1) = ( -1)^{m +k} \pmod p$.
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
28644
For $q, p$ odd primes such that $p \neq q$, there is not primitive root modulo $pq$.
128584
Sum of squared quadratic non-residues
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
25910
Product of Quadratic Residues
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$