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Exactly one of the numbers a+b and |a-b| belongs to X

Source: Tuymaada 2008, Senior League, Second Day, Problem 6.

July 18, 2008

combinatorics unsolvedcombinatorics

Problem Statement

A set

X

of positive integers is called nice if for each pair

a

b\in X

exactly one of the numbers a \plus{} b and |a \minus{} b| belongs to

X

(the numbers

a

and

b

may be equal). Determine the number of nice sets containing the number 2008. Author: Fedor Petrov