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Romania TST 2016 Day 3 P1

Source: Romania TST 2016 Day 3 P1

November 1, 2017
algebranumber theory

Problem Statement

Given a positive integer nn, determine all functions ff from the first nn positive integers to the positive integers, satisfying the following two conditions: (1) ∑k=1nf(k)=2n\sum_{k=1}^{n}{f(k)}=2n; and (2) ∑k∈Kf(k)=n\sum_{k\in K}{f(k)}=n for no subset KK of the first nn positive integers.
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