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National and Regional Contests
Romania Contests
JBMO TST - Romania
2022 Junior Balkan Team Selection Tests - Romania
P5
P5
Part of
2022 Junior Balkan Team Selection Tests - Romania
Problems
(1)
Romania Junior TST 2022 Day 1 P5
Source: Romania JBMO TST 2022
4/20/2022
We call a set
A
⊂
R
A\subset \mathbb{R}
A
⊂
R
free of arithmetic progressions if for all distinct
a
,
b
,
c
∈
A
a,b,c\in A
a
,
b
,
c
∈
A
we have
a
+
b
≠
2
c
.
a+b\neq 2c.
a
+
b
=
2
c
.
Prove that the set
{
0
,
1
,
2
,
…
3
8
−
1
}
\{0,1,2,\ldots 3^8-1\}
{
0
,
1
,
2
,
…
3
8
−
1
}
has a subset
A
A
A
which is free of arithmetic progressions and has at least
256
256
256
elements.
combinatorics
Romanian TST