$a|b^2$ , $b^2|a^3$ , $a^3|b^4$ , $b^4| a^5$... then...
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
152436
Are $(x^3)^{1/3} $ and $\sqrt{x^2}$ monomials?
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
4333
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
5981
For which values of $a$ does $a-2 \mid a^3+4$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
92975
Does $a^n \mid b^n$ imply $a\mid b$?