Problem A. 761. (November 2019)

A. 761. Let \(\displaystyle n \ge 3\) be a positive integer. We say that a set \(\displaystyle S\) of positive integers is good if \(\displaystyle |S| = n\), no element of \(\displaystyle S\) is a multiple of \(\displaystyle n\), and the sum of all elements of \(\displaystyle S\) is not a multiple of \(\displaystyle n\) either. Find, in terms of \(\displaystyle n\), the least positive integer \(\displaystyle d\) for which there exists a good set \(\displaystyle S\) such that there are exactly \(\displaystyle d\) nonempty subsets of \(\displaystyle S\) the sum of whose elements is a multiple of \(\displaystyle n\).

Proposed by Aleksandar Makelov, Burgas, Bulgaria and Nikolai Beluhov, Stara Zagora, Bulgaria

(7 pont)

Deadline expired on December 10, 2019.

Statistics:

7 students sent a solution.
7 points:	Weisz Máté.
3 points:	2 students.
1 point:	4 students.

Problems in Mathematics of KöMaL, November 2019