How to prove that $(k_{1}k_{2}...k_{n}) \equiv (z_{1}z_{2}...z_{n})\mod n$ if they are both complete system of residues modulo n.?
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
108237
Show $a^p \equiv b^p \mod p^2$
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
47148
Complete balanced (signed) residue System of an odd modulo m
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
6160
How to prove a number $a$ is quadratic residue modulo $n$?
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
41673
Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$