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Even Number Of Representations

Source: KöMaL A. 830

October 11, 2022

number theorykomal

Problem Statement

For

H\subset \mathbb Z

and

n\in\mathbb Z

let

h_n

denote the number of finite subsets of

H

in which the sum of the elements is

n

. Determine whether there exists

H\subset \mathbb Z

for which

0\notin H

and

h_n

is a finite even number for every

n\in\mathbb{Z}

. (The sum of the elements of the empty set is

0

.)
Proposed by Csongor Beke, Cambridge

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