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Serbia Contests
Serbia Team Selection Test
1981 Yugoslav Team Selection Test
Problem 1
Problem 1
Part of
1981 Yugoslav Team Selection Test
Problems
(1)
increasing arithmetic sequences in set
Source: Yugoslav TST 1981 P1
5/29/2021
Let
n
≥
3
n\ge3
n
≥
3
be a natural number. For a set
S
S
S
of
n
n
n
real numbers,
A
(
S
)
A(S)
A
(
S
)
denotes the set of all strictly increasing arithmetic sequences of three terms in
S
S
S
. At most, how many elements can the set
A
(
S
)
A(S)
A
(
S
)
have?
arithmetic sequence
combinatorics