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products of two different numbers from n different reals

Source: (2022 -) 2023 XVI Dürer Math Competition Regional E5

May 25, 2024
number theory

Problem Statement

Let n≥3n \ge 3 be an integer. Timi thought of nn different real numbers and then wrote down the numbers which she could produce as the product of two different numbers she had in mind. At most how many different positive prime numbers did she write down (depending on nn)?
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