IMO 2023 Shortlist A3

Let x1,x2,...,x2023 be distinct real positive numbers such that an “ d px1 x2 ¨¨¨ xnq ˆ x1 x2 ¨¨¨ xn ˙ is an integer for...

imomathematicsolympiadshortlistalgebra

IMO 2023 Shortlist A3

Category: Algebra

Problem

Let x1,x2,...,x2023 be distinct real positive numbers such that an “ d px1 x2 ¨¨¨ xnq ˆ x1 x2 ¨¨¨ xn ˙ is an integer for every n “ 1,2,...,2023. Prove that a2023 ě 3034. (Netherlands)