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KoMaL A Problems
KoMaL A Problems 2022/2023
A. 830
A. 830
Part of
KoMaL A Problems 2022/2023
Problems
(1)
Even Number Of Representations
Source: KöMaL A. 830
10/11/2022
For
H
⊂
Z
H\subset \mathbb Z
H
⊂
Z
and
n
∈
Z
n\in\mathbb Z
n
∈
Z
let
h
n
h_n
h
n
denote the number of finite subsets of
H
H
H
in which the sum of the elements is
n
n
n
. Determine whether there exists
H
⊂
Z
H\subset \mathbb Z
H
⊂
Z
for which
0
∉
H
0\notin H
0
∈
/
H
and
h
n
h_n
h
n
is a finite even number for every
n
∈
Z
n\in\mathbb{Z}
n
∈
Z
. (The sum of the elements of the empty set is
0
0
0
.)Proposed by Csongor Beke, Cambridge
number theory
komal