MathDB
Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
2017 Mexico National Olympiad
2
2
Part of
2017 Mexico National Olympiad
Problems
(1)
Integer average set
Source: Mexico National Olympiad 2017, Problem 2
11/6/2017
A set of
n
n
n
positive integers is said to be balanced if for each integer
k
k
k
with
1
≤
k
≤
n
1 \leq k \leq n
1
≤
k
≤
n
, the average of any
k
k
k
numbers in the set is an integer. Find the maximum possible sum of the elements of a balanced set, all of whose elements are less than or equal to
2017
2017
2017
.
number theory
Average