$9 \mid a^2 +b^2+ab$. Show that $3$ divides both $a$ and $b$.
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
117167
$3^{n+1}$ divides $2^{3^n}+1$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
49687
Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
89184
Prove $30|(a^3b-ab^3) $
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
92975
Does $a^n \mid b^n$ imply $a\mid b$?
118574
prove that $24 \mid a(a^2-1)$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
12100
$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?