This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 5802

2024 USA IMO Team Selection Test, 3
Let $n>k \geq 1$ be integers and let $p$ be a prime dividing $\tbinom{n}{k}$. Prove that the $k$-element subsets of $\{1,\ldots,n\}$ can be split into $p$ classes of equal size, such that any two subsets with the same sum of elements belong to the same class. [i]Ankan Bhattacharya[/i]
bye combinatorics number theory bijection factorization generating functions mathematical induction modular arithmetic p-adic valuation

2005 IberoAmerican Olympiad For University Students, 1
Let $P(x,y)=(x^2y^3,x^3y^5)$, $P^1=P$ and $P^{n+1}=P\circ P^n$. Also, let $p_n(x)$ be the first coordinate of $P^n(x,x)$, and $f(n)$ be the degree of $p_n(x)$. Find \[\lim_{n\to\infty}f(n)^{1/n}\]
limit ratio induction polynomial algebra analytic geometry limits mathematical induction polynomials