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max different xy = prime. combo NT

Source: (2022 -) 2023 XVI Dürer Math Competition Regional E+3

May 25, 2024
combinatoricsnumber theory

Problem Statement

Let n≥3n \ge 3 be an integer and AA be a subset of the real numbers of size n. Denote by BB the set of real numbers that are of the form x⋅y x \cdot y, where x,y∈Ax, y \in A and x≠yx\ne y. At most how many distinct positive primes could BB contain (depending on nn)?
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