How can I show that $\begin{cases} x = 2 \pmod 6 \\ x = 5 \pmod 8 \end{cases}$ does not have a solution?
68252
Chinese Remainder Theorem solvability for non-coprime moduli
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
41655
Simple equation for $x$ but getting no proof.
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
94407
Number of solutions for $x[1] + x[2] + \ldots + x[n] =k$
51153
Number of solutions to $x^2\equiv a\pmod m$
52706
Can Reduce *really* not solve for x here?
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
20221
Combinatorics - Removing Double Counted Cases
96398
An integer $a \pmod m$ has inverse if and only if $\gcd(a,m)=1$?
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
41418
$2+2 = 5$? error in proof
18093
Find $x$ such that $\sum_{k=1}^{2014} k^k \equiv x \pmod {10}$
131731
Primes that can't be written as sum of two squares. Mod
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
15897
Solve a congruence $1978^{20}\equiv x\pmod{125}$