Why Are Congruence Relations Written as $”a\equiv b \pmod m”$
7043
mod [= remainder] operation (and relation), name and meaning
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
45882
Solving a congruence without Fermat's little theorem
158025
Intuition of why $\gcd(a,b) = \gcd(b, a \pmod b)$?
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
36713
Solving multiple congruences by CRT = Chinese Remainder Theorem
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
115435
Induction: prove using congruences
141369
If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
12636
Product Rule for mod operator: $ ab\bmod p = ((a\bmod p)(b\bmod p))\bmod p$
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
30725
Why are naturals < modulus equal if congruent? [uniqueness of remainder]
15897
Solve a congruence $1978^{20}\equiv x\pmod{125}$