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OMCPLP 2024 Problem 2

  • Day 1

Para cada conjunto de cinco inteiros S={a1,a2,a3,a4,a5}S = \{a_1, a_2, a_3, a_4, a_5\}, seja PSP_S o produto de todas as diferenças entre dois deles, isto é,

PS=(a5−a1)(a4−a1)(a3−a1)(a2−a1)(a5−a2)(a4−a2)(a3−a2)(a5−a3)(a4−a3)(a5−a4)P_S = (a_5 - a_1)(a_4 - a_1)(a_3 - a_1)(a_2 - a_1)(a_5 - a_2)(a_4 - a_2)(a_3 - a_2)(a_5 - a_3)(a_4 - a_3)(a_5 - a_4)

Determine o maior inteiro nn tal que, dado qualquer conjunto SS de cinco inteiros, nn divide PSP_S.

Official text Lusophon Mathematical Olympiad 2024 official paper, page 1. Quoted with source.

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