If $a\mid b^2, b^2\mid a^3,\ldots ,a^n\mid b^{n+1},b^{n+1}\mid a^{n+2},\ldots$ then $a=b$
91178
chain of divisibility relation
130488
Prove by induction that $3\mid n^3 - n$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
48211
When is $(a+b)^n \equiv a^n+b^n$?
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
92975
Does $a^n \mid b^n$ imply $a\mid b$?