Skip to main content
TheBestMagician's user avatar
TheBestMagician's user avatar
TheBestMagician's user avatar
TheBestMagician
  • Member for 3 years, 10 months
  • Last seen this week
21 votes
Accepted

Sum of angles under which a fixed line segment is seen from points situated on another line segment

13 votes
Accepted

How many $3$-element subsets of $\{1,2,3,...,19,20\}$ have product divisible by $4$?

12 votes
Accepted

In a triangle, lines are drawn from each vertex to the opposite side. Can there be seven regions of integer area?

10 votes

Interesting ways to write 2023

6 votes
Accepted

Find all integer polynomials $f(x)$ such that $f(n)\mid 2^n-1$ for all $n\in\mathbb{N}^+$.

5 votes
Accepted

Find function $ f $ such that $f(\frac{x-3}{x+1})+f(\frac{x+3}{1-x})=x$

5 votes

For a triangle, prove that $\frac{1}{AE\cdot BE}+ \frac{1}{CG\cdot BG}+ \frac{1}{AF\cdot CF}=\frac{1}{r^2} $

4 votes

Find the area of rhombus $ABCD$

4 votes

In an equilateral triangle, lines are drawn from each vertex to the opposite side. Can there be seven regions of integer area?

3 votes
Accepted

An Olympiad Question on cube roots.

3 votes
Accepted

Prove that the 5-adic valuation of $(10^{k+t}+10^t+1)^c-1$ is $t+v_5(c)$

3 votes
Accepted

IMO proposal question. prove $\sum_{k=1}^{n} k \cos(\frac{2 \pi a_k} n) = 0$

3 votes

Evaluate $\sum_{r=0}^n 2^{n-r} \binom{n+r}{r}$

3 votes

Prove $a^2 + b^2 + c^2 + ab + bc +ca \ge 6$ given $a+b+c = 3$ for $a,b,c$ non-negative real.

3 votes

Is there a nice way to simplify $ \frac{\sin x \theta}{\sin \theta}-\frac{\cos x \theta}{\cos \theta}=x-1 $ to get solutions?

3 votes

How can I prove that $\lim_{k\to\infty}L(k+1,k)=\pi$?

3 votes

Proof of divisibility by 18 by induction

3 votes
Accepted

How does one find values of $m$ for which the roots of $2x^2-mx-8=0$ differ by $m-1$

3 votes
Accepted

How can I prove that, if $x,y,z>0$ and $xyz=1$, then $2(x^2+y^2+z^2)+9\geq 5(x+y+z)$

3 votes

Proving $ e^2 = e$?

3 votes

Prove that there exists a $100 \times 100$ square with no integer point visible from the origin.

3 votes

Is it possible to place $1995$ natural numbers on along a circle such that for two of these numbers the ratio of the greatest to the least is a prime?

3 votes
Accepted

A combinatorial question involving two pairs of sums

3 votes
Accepted

"Inverse" of the inscribed angle theorem

2 votes
Accepted

Trying to evaluate $\int \frac{1}{\sin(x)\cos^3(x)} \,dx$ and got stuck

2 votes
Accepted

Change of variables for summation fails

2 votes

Solve $\lfloor x \rfloor ^2 + 9 \{x\}^2=6x-10, \forall x \in \mathbb{R}$

2 votes
Accepted

prove that the maximum value of a function is attained when all $x_i$'s are 0 or 1

2 votes
Accepted

Prove the difference between an integer and its permutation is a composite number.

2 votes

Question about a sequence $a_{n+1}=2^{a_n}-1$