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A, B subests of 1-100, n \in A => 2n + 2 \in B

Source: 2015 Cuba 1.4

September 20, 2024

number theory

Problem Statement

Let

A

and

B

be two subsets of

\{1, 2, 3, 4, ..., 100\}

, such that

|A| = |B|

and

A\cap B =\emptyset

. If

n \in A

implies that

2n + 2 \in B

, determine the largest possible value of

|A \cup B|

.

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