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Miklós Schweitzer
2012 Miklós Schweitzer
2
2
Part of
2012 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 2012 P2
Source: Miklós Schweitzer 2012 P2
8/20/2018
Call a subset
A
A
A
of the cyclic group
(
Z
n
,
+
)
(\mathbb{Z}_n,+)
(
Z
n
,
+
)
rich if for all
x
,
y
∈
Z
n
x,y \in \mathbb{Z}_n
x
,
y
∈
Z
n
there exists
r
∈
Z
n
r \in \mathbb{Z}_n
r
∈
Z
n
such that
x
−
r
,
x
+
r
,
y
−
r
,
y
+
r
x-r,x+r,y-r,y+r
x
−
r
,
x
+
r
,
y
−
r
,
y
+
r
are all in
A
A
A
. For what
α
\alpha
α
is there a constant
C
α
>
0
C_\alpha>0
C
α
>
0
such that for each odd positive integer
n
n
n
, every rich subset
A
⊂
Z
n
A \subset \mathbb{Z}_n
A
⊂
Z
n
has at least
C
α
n
α
C_\alpha n^\alpha
C
α
n
α
elements?
linear algebra