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math110
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I am a Middle school competition teacher

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280
How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?
114
Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square
108
How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$
100
Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$
82
How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$