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increasing arithmetic sequences in set

Source: Yugoslav TST 1981 P1

May 29, 2021
arithmetic sequencecombinatorics

Problem Statement

Let n≥3n\ge3 be a natural number. For a set SS of nn real numbers, A(S)A(S) denotes the set of all strictly increasing arithmetic sequences of three terms in SS. At most, how many elements can the set A(S)A(S) have?
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