Nikola Tolzsek's user avatar
Nikola Tolzsek's user avatar
Nikola Tolzsek's user avatar
Nikola Tolzsek
  • Member for 4 years, 1 month
  • Last seen more than a week ago
4 votes
1 answer
257 views

Proving 4 points on a circle.

4 votes
0 answers
3k views

Intriguing moves with the $3\times3\times3$ Rubiks cube

4 votes
2 answers
239 views

Calculate the ratio based on the lengths of edges of triangle

3 votes
1 answer
112 views

Proving $a^i+i$ is a complete residue system if $n | a^n-1$ [duplicate]

3 votes
2 answers
359 views

Find the maximum value of $P= \frac2{1+a^2}-\frac2{b^2+1}+\frac3{c^2+1}$

3 votes
2 answers
125 views

Prove that there exists 3 numbers $a,b,c$ so that $P(a)=b, P(b)=c, P(c)=a$

3 votes
1 answer
56 views

Find all the values of a so that $3^{ \lfloor \frac{n-1}{2} \rfloor }\mid P_n{(a^3)}$ given the definition of $P_n$

3 votes
1 answer
293 views

A Polynomial-Inequality problem from Vietnam National Olympiad 2021

3 votes
0 answers
117 views

Number of ways to mark the edges of a net of regular tetrahedra

2 votes
1 answer
147 views

A simple counting and restricting the case from Vietnam National Olympiad 2021

2 votes
2 answers
145 views

Quadratic Function from the Taiwan IMO TST 2005

2 votes
1 answer
385 views

The spreading game and its expansion

2 votes
2 answers
65 views

A fantasy game on the Angels&Demons novel

2 votes
2 answers
172 views

A game of tourism

2 votes
3 answers
139 views

Find all $f(x)$ such that $x(f(x+1)-f(x))=f(x)$

2 votes
1 answer
177 views

Find $P(-\frac{1}{2})$ given a infinite points of a polynomial

2 votes
2 answers
123 views

Find the limit of $U_{n+1}=\frac13 (U_n+U_{n-1}^2+\frac59)$

2 votes
1 answer
94 views

Find the limit of $\frac{T_n}{5n+4}$

2 votes
1 answer
76 views

Find the limit of $\frac{2+\sqrt{2U_n^2+4U_n+4}}{U_n}$

1 vote
1 answer
814 views

Find all $f: \mathbb{R} \to \mathbb{R}$ such that $(f(x)+y)(f(x-y)+1)=f(f(xf(x+1))-yf(y-1)), \forall x,y \in \mathbb{R}$

1 vote
0 answers
32 views

Find all $m$ such that there exists $P,Q,R$ satisfying polynomial conditions

1 vote
3 answers
145 views

Find the limit given that $f(1)=1$, $f(x+y)=f(x)+f(y)+2xy$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^4}$

1 vote
1 answer
88 views

Prove the irreducibility of $P(x)$ which satisfies: $xP(x-1)=(x-2022)P(x)+2022$

1 vote
3 answers
150 views

Find the largest value of $P=\frac{3x+2y+1}{x+y+6}$

1 vote
0 answers
123 views

Prove that $\sum_{cyc} \frac{1}{5a^2-4a+11} \le \frac{1}{4}$

1 vote
1 answer
106 views

Find the greatest value of $P= \frac{2x^2}{1+x^2} -\frac{2y^2}{1+y^2}+\frac{3z^2}{1+z^2}$

1 vote
1 answer
249 views

A problem on the $n\times n$ square [closed]

1 vote
1 answer
113 views

Proving a monotonic subsequence exists

1 vote
2 answers
69 views

A mathematic insights to Calendar.

1 vote
2 answers
552 views

Find the best strategy for a card game