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Mathematics
Witold's user avatar
Witold's user avatar
Witold's user avatar
Witold
  • Member for 5 years, 1 month
  • Last seen more than 1 year ago
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15
Interesting inequality $\frac{x^{m+1}+1}{x^m+1} \ge \sqrt[2m+1]{\frac{1+x^{2m+1}}{2}}$
Jun 7, 2019
14
Winning strategy in a game with the positive divisors of $10^n$
May 24, 2020
11
Packing of parallelograms with sides $1$ and $\sqrt{2}$ and angle $45^{\circ}$ in a rectangular container
Jun 25, 2019
10
Independence problem: one rook and maximum number of knights on the chessboard $8 \times 8$
Jun 10, 2019
10
Interesting four-sum inequality $n^2 \left(\sum \limits_{k=1}^n \frac{k+1}{k}\right) \left( \sum \limits_{k=1}^n \frac{k}{k+1}\right) \ge...$
Aug 3, 2019
9
Isolating frequencies and phases of superposed cosine functions
Dec 24, 2021
7
Find an example of a set of points of the plane such that there exist at least $2^{n-2}$ good partitions.
Jun 24, 2019
7
Proving that every positive integer is of the form $x^2+y^2-5z^2$
Oct 25, 2020
6
Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$
Aug 2, 2019
6
Functional equation $f(f(x)y+x)=f(x)f(y)+f(x)$
Nov 26, 2019