For any composite modulus $n$, there are two consecutive integers whose product $\equiv 0 \bmod n$
102112
Idempotents in $\mathbb Z_n$
68252
Chinese Remainder Theorem solvability for non-coprime moduli
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
87626
Why are all $n$, s.t. the sum of digits of $n$ and $n^2$ coincide, $\equiv 0,1 \bmod 9$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
19071
solution set for congruence $x^2 \equiv 1 \mod m$
141369
If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
107990
Does there exist an integer $x$ satisfying the following congruences?
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
105405
Product of three consecutive positive integers is never a perfect power
30725
Why are naturals < modulus equal if congruent? [uniqueness of remainder]
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$