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: 1

1996 French Mathematical Olympiad, Problem 5
Tags: france , combinatorics , number theory
Let $n$ be a positive integer. We say that a natural number $k$ has the property $C_n$ if there exist $2k$ distinct positive integers $a_1,b_1,\ldots,a_k,b_k$ such that the sums $a_1+b_1,\ldots,a_k+b_k$ are distinct and strictly smaller than $n$. (a) Prove that if $k$ has the property $C_n$ then $k\le \frac{2n-3}{5}$. (b) Prove that $5$ has the property $C_{14}$. (c) If $(2n-3)/5$ is an integer, prove that it has the property $C_n$.