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number of arabic subsets of {1,2, ..., n} has the same parity as n

Source: 2018 Saudi Arabia IMO TST III p2

July 28, 2020
number theory

Problem Statement

A non-empty subset of {1,2,...,n}\{1,2, ..., n\} is called arabic if arithmetic mean of its elements is an integer. Show that the number of arabic subsets of {1,2,...,n}\{1,2, ..., n\} has the same parity as nn.
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