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This is a question I first heard from Ori Pomerantz.
Part 1Consider all naturals from 2 and up, and divide them into two sets, A and B. Prove that in at least one of these sets there are three distinct numbers, a, b and c, such that ab=c.Part 2Show how to construct such a division into two infinite sets A and B so that only one of them will have such an a, b, c triplet.Solve both questions to appear on the solvers' list. |
List of solvers:James Ge (1 December 23:59)Itsik Horovitz (2 December 10:23) Gaoyuan Chen (2 December 20:42) Li Wei (3 December 05:19) Oded Margalit (3 December 23:09) Omer Angel (4 December 05:57) Shmuel Menachem Spiegel (4 December 15:15) Øyvind Grotmol (6 December 06:50) Ori Pomerantz (6 December 15:24) Anurag Anshu (6 December 20:08) Miao Hua (8 December 17:58) Pei Wu (9 December 13:46) Dan Dima (10 December 22:49) Bojan Bašić (12 December 04:17) Ante Turudić (14 December 23:36) Harsha HS (16 December 21:38) Ante Kovačić (17 December 12:10) Victor Chang (17 December 13:48) Hongcheng Zhu (26 December 18:51) |
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