MEMO 2014 ekipno problem 7
Kvaliteta:
Avg: 1,0Težina:
Avg: 5,0 A finite set of positive integers
is called meanly if for each of its nonempty subsets the arithmetic mean of its elements is also a positive integer. In other words, A is meanly if
is an integer whenever
and
are distinct.
Given a positive integer
, determine the least possible sum of the elements of a meanly
-element set.
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![\frac{1}{k}(a_1 + \ldots + a_k)](/media/m/0/9/d/09d915c9a017f0e013d62a4d8d852ed8.png)
![k \geq 1](/media/m/4/7/4/474e08320ac4dfd51b6214797b6d06be.png)
![a_1, \ldots, a_k \in A](/media/m/d/8/1/d8103ae83ea86e171a783e5945bf7d7f.png)
Given a positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
Izvor: Srednjoeuropska matematička olimpijada 2014, ekipno natjecanje, problem 7