All Questions
9
questions with no upvoted or accepted answers
7
votes
0
answers
180
views
Pairwise sums are equal
The distinct positive integers $a_1,a_2,...,a_n,b_1,b_2,...,b_n$ with $n\ge2$ have the property that the $\binom{n}2$ sums $a_i+a_j$ are the same as the $\binom{n}2$ sums $b_i+b_j$ (in some order). ...
- 2,325
5
votes
0
answers
2k
views
Good books to learn olympiad geometry,number theory, combinatorics and more
I want to start learning olympiad mathematics more seriously, and I would like to have advice on some good books or pdfs to learn with.
I have background but not a big background. For example I know ...
- 2,510
3
votes
0
answers
126
views
After $2013$ such transformations, how many number $2013$ are there on the line if the given numbers are $1$ and $1000$?
Several natural numbers are given on a line, we perform a transformation as follow:for every pair of consecutive integers on the line, write sum of those two numbers in the middle of them. After $2013$...
- 4,135
2
votes
1
answer
178
views
Divisibility of a summation
Let $n , l, k, p$ be positive integers, and $1\leq p\leq n$. Let $B(n, l, k, p)$ be the cardinality of the following set
\begin{eqnarray}
\{(a_1, a_2, \cdots, a_n)\in\mathbb{Z}^{\oplus n}|\ \ 0\leq ...
- 699
1
vote
0
answers
123
views
PDFs for Olympiad preparation
Could someone please recommend me some pdf files containing theory for topics that come up often in maths olympiads? I'm currently working through one about inequalities, and I'm really enjoying it. I ...
- 41
1
vote
0
answers
346
views
Limit in Olympiad discursive question
Let $M,k$ be two positive integers. Define $X_{M,k}$ as the set of the numbers $p_1^{\alpha_1}\cdot p_2^{\alpha_2} \cdots p_r^{\alpha_r}$ where $p_i$ are prime numbers such that $M \leq p_1 < p_2 &...
- 2,314
1
vote
1
answer
342
views
Count ways to distribute candies
N students sit in a line, and each of them must be given at least one candy. Teacher wants to distribute the candies in such a way that the product of the number of candies any two adjacent students ...
- 272
0
votes
0
answers
90
views
Number of 1-runs
A binary string is a word containing only $0$s and $1$s. In a binary string, a
1-run is a non-extendable substring containing only $1$s. Given a positive
integer n, let B(n) be the number of $1$-runs ...
0
votes
0
answers
76
views
Combinatorics with Bashy
We call a set of positive integer good, if the greatest common divisor of all of the elements in this set is $1$.
$a_n$ is the number of good subsets of $\{1,2,...,n\}$. Find all integer $n \ge 2019$, ...
- 4,266