For what integer values $a$ does the system of congruences have *at least one solution*?
2904
Solving linear congruence (modular inverse or fraction) via gcd Bezout equation
8446
Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$
96095
If $\{a_1,\dots,a_{\phi(n)}\}$ is a reduced residue system, what is $a_1\cdots a_{\phi(n)}$ congruent to?
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
143754
Finding the solution of the congruence $4x\equiv16\pmod{26}$
56803
Finding solutions to congruence equations
33314
How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
108035
solving diophantine equations using congruences
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
51153
Number of solutions to $x^2\equiv a\pmod m$
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
81267
A simple doubt in number theory problem.
45882
Solving a congruence without Fermat's little theorem