My Question is how does this proof workout? Unable to understand $m\mid n$ and its relation to $a$ and $b$
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
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
29692
Proof verification: elementary Number Theory Proof of $am+bn = 1$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
123056
Help in understanding the proof of Mersenne Prime
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
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$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$