Congruence question; please help.
108238
Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$.
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
18245
How to check if a system of congruence is solvable?
80535
Linear congruence fill in the missing step?
19761
Show for prime numbers of the form $p=4n+1$,  $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.
57654
Congruent Modulo $n$: definition
22029
Solving modular arithmetic questions
40892
How to solve a linear congruence $8n+9\equiv 0\pmod{\!1163}$
149759
Problem on multiplication formulae.
85449
Show a,b,c congruences when $a^2+b^2=c^2$
14668
complex number question involving modulus
42754
Modular arithmetic: division, fractions, solving linear congruences
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
128634
Doubt related to a theorem in congruences of Chapter 5 of Apostol Introduction to analytic number theory
8481
System of congruence relations
42723
Lattices are congruence-distributive
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