How do I see that $a^2 \equiv 1 \mod{( p \cdot q)}$ has four incongruent solutions?
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
77990
How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?
122741
$x^2$ is congruent to $-1 \bmod p$
36611
Algorithms for solving the discrete logarithm $a^x \equiv b\pmod{n}$ when $\gcd(a,n) \neq 1$
24837
$x^2+1=0$ uncountable many solutions
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
68635
When is $2$ a quadratic residue mod $p$?
102234
Show $a^p \equiv a \mod 2p$
103304
Finding the number of solutions to a diophantine equation
83753
Why $\,p \cdot (p^{-1} \mod q) + q \cdot (q^{-1} \mod p) = pq + 1$?
102204
Factoring product of two primes from solutions of congruence
15314
Number of solutions to $x^n \equiv 1 \mod p$
94965
Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$
20034
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
56803
Finding solutions to congruence equations
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)