Solve $\frac{A^2 + B^2}{AB + 1} = K$ for integral values of $A$, $B$, & $K$. Prove that $K$ is a perfect square
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
52672
Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
110408
Solving for $A$ in $Ax = b$
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
14480
Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
103555
Find all positive integral soludions of $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 4$
36837
Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$
82016
Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
143093
Determining k: $\int_{6}^{16} \frac{dx}{\sqrt{x^3 + 7x^2 + 8x - 16}} = \frac{\pi}{k}$
69874
Are there any integer solutions to $a^3=b^2$?
137015
Solutions for $a^2+b^2+c^2=d^2$
20834
Integer solutions to $c=a^2-b^2$