Все публикации

0:09:55

Quadratic equation with ten 1-s and ten 2-s.

0:07:35

A single---line solution of a trigonometric equation

0:06:54

A simply evaluated monstrous sum.

0:16:23

Another calculus problem from Putnam 2005 competition.

0:03:32

A simple problem with a smart solution. Can we cover a 10×10 square with 1×4 tiles?

0:04:37

The exact value of cos(π/7) cos(2π/7) cos(4π/7) cos(8π/7) cos(16π/7) cos(32π/7)

0:11:33

Putnam 2005. Another application of Feynman's trick. Integral of ln(x+1)/(x²+1) in (0,1).

0:09:53

Integral of sin(x)/x in the interval (0,1). Feynmans' trick not involving complex numbers.

0:08:04

An equation containing 2023 exponentiations of x and number π

0:00:58

Odd Balls

0:07:59

A segment dividing the median in given ratio

0:05:05

The Christmas Tree Problem

0:14:01

Geometric proofs of some non-geometric facts. Algebraic identities.

0:16:40

The least number with sum of digits equal to 10 in numeric systems base both 10 and 8.

0:07:37

In triangle ABC find point К so that triangles AKB, BKC and AKC have same area. Two methods.

0:07:42

Ratio of the sum of inverse cubes of all positive integers to the ones neither multiples of 2 nor 3.

0:01:00

Can an irrational power of an irrational number be RATIONAL?

0:00:53

Find the greatest power of 2 dividing a number of type 10...064 with an arbitrary number of zeroes.

0:07:00

Find the positive (real) root of an equation: ∛(20x+22) − ∛(20x−2) = 2

0:15:00

Three powers of 4 added to a perfect square

0:04:24

Another motion problem solved in a purely arithmetic way

0:01:00

Prove that in any triangle a bisector is always located between the altitude and the median.

0:11:49

Is ⌊(44+√2022)¹⁰⁰⁰⁰⁰⁰⌋ even or odd?

0:01:00

Prove that fraction (21n+4)/(14n+3) is in lowest terms. From the very first IMO (1959)