Leox's user avatar
Leox's user avatar
Leox's user avatar
Leox
  • Member for 10 years, 6 months
  • Last seen this week
  • Ukraine
13 votes
2 answers
540 views

Derive the recurrence relations

11 votes
2 answers
342 views

Solve the functional equation $\frac{f(x)}{f(y)}=f\left( \frac{x-y}{f(y)} \right)$

10 votes
5 answers
2k views

Find all prime solutions of equation $5x^2-7x+1=y^2.$

9 votes
1 answer
310 views

How to represent Fermat number $F_n$ as a sum of three squares?

9 votes
6 answers
726 views

Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $

8 votes
2 answers
1k views

$p$-adic valuation of harmonic numbers

7 votes
1 answer
583 views

Product of consecutive natural numbers

7 votes
1 answer
212 views

Find eigenvectors of the $(n+1) \times (n+1)$-matrix

7 votes
1 answer
278 views

Find $A^m B^n$ for noncommutative variables

6 votes
1 answer
192 views

Find two-index Inverse relations

6 votes
2 answers
199 views

Find eigenvalues of the matrix

6 votes
2 answers
117 views

Prove the identity $ \sum\limits_{i=k}^{n} \frac{1}{(i-k)! (a+i)_{n-i}}={\frac {a+n}{ \left( a{+} k \right) (n{-}k)! } }.$

6 votes
2 answers
800 views

Number of invertible matrices over finite rings

6 votes
1 answer
13k views

In how many ways can we arrange $6$ red, $3$ blue and $4$ green balls in a row such that there is no adjacent green balls?

6 votes
2 answers
177 views

How can I use these two bijections to form a bijection $\mathbb{R}^{\mathbb{N}} \to \mathbb{R}$?

6 votes
9 answers
597 views

How to construct a bijection $\mathbb{N} \to \mathbb{N} \times \{0, 1\}.$

5 votes
1 answer
83 views

Two sequences $a_{2n}=a_n+1, a_{2n+1}=a_{n}+2$ and $b_{3n}=b_n+1, b_{3n+1}=b_n+2, b_{3n+2}=b_n+3$

5 votes
2 answers
753 views

Decomposition of representation of symmetric group

5 votes
3 answers
3k views

Probability of a path of a given length between two vertices of a random graph

5 votes
2 answers
110 views

Prove the inequality $a^3+2 \geq a^2+2 \sqrt{a}$

5 votes
2 answers
524 views

Find trace of linear operator

5 votes
2 answers
197 views

How to prove the inequality $(1+a+a^2)(1+b+b^2)(1+c+c^2) \leq (1+a+b^2)(1+b+c^2)(1+c+a^2)?$

5 votes
2 answers
91 views

Prove the identity $ \sum\limits_{k=0}^{n-1} (-1)^{k} \binom{n}{k} (n-k) \frac{(a+k-2)!}{(a+k-n)!}=0.$

5 votes
0 answers
99 views

Interesting property of Fibonacci numbers

5 votes
1 answer
518 views

Solve the diophantine equation $3\,{a}^{3}b-13\,{b}^{3}-26\,a-24\,b=0.$

5 votes
3 answers
4k views

Formula for length of the diagonal of a parallelepiped

5 votes
3 answers
634 views

Solve the system of linear inequalities with parameters

5 votes
2 answers
86 views

Double integral over the hypocycloid

4 votes
1 answer
124 views

What is the series $ \dfrac{1}{\left( x-{y}^{2} \right) \left(1- yx \right) \left( {x}^{2}-y \right)} $ expansion?

4 votes
2 answers
148 views

Find $ k$ last digits of quotient

1
2 3 4 5 6