Solve $x^2 \equiv -1 \pmod{41} $
122741
$x^2$ is congruent to $-1 \bmod p$
36713
Solving multiple congruences by CRT = Chinese Remainder Theorem
155743
Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
45882
Solving a congruence without Fermat's little theorem
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
145617
Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?
22029
Solving modular arithmetic questions
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
65849
What are the common solutions of $x^2+y=31$ and $y^2+x=41$?
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
42032
Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$
119630
For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
155012
Solving quadratic equations in modular arithmetic