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math110
  • Member for 11 years, 4 months
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I am a Middle school competition teacher

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question
43
Proving $\sum_{i=1}^{n}\sum_{j=1}^{n}\left\{\frac{x_{i}}{x_{j}}\right\}\le \frac{9}{14}n^2$？
Jan 3
question
38
A family of polynomials whose zeros all lie on the unit circle
May 3, 2018
question
24
This inequality why can't solve it by now (Only four variables inequality)?
Jan 12, 2015
question
24
show this nice and hard inequality with $ \prod_{i=1}^{n}|x_{i}-y_{i}|<e^{\frac{n}{2}}$
Oct 11, 2018
question
24
Is $\iiint_{[0, 1]^3} \lvert f(x)+f(y)+f(z)\rvert\, dx\, dy\, dz \ge \int_0^1 \lvert f(x)\rvert\, dx$?
Feb 5, 2021
question
20
When is $1^n+2^n+3^n+4^n+\cdots+n^n$ a square number?
Mar 5, 2018
question
18
An inequality concerning Lagrange's identity
May 19, 2016
question
16
Solve this Diophantine equation $(2^x-1)(3^y-1)=2z^2$
Apr 1, 2018
question
14
Find all solution $a,b,c$ with $(1-a^2)(1-b^2)(1-c^2)=8abc$
Jun 5, 2015
answer
13
A variant of Cauchy-type functional equation conjecture
Oct 15, 2018
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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: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$