MathDB

4

Part of 2005 Mexico National Olympiad

Problems(1)

an arithmetic trio a_i, a_j, a_k if i < j < k and 2a_j = a_i + a_k.

Source: Mexican Mathematical Olympiad 2005 OMM P4

7/31/2018
A list of numbers a1,a2,…,ama_1,a_2,\ldots,a_m contains an arithmetic trio ai,aj,aka_i, a_j, a_k if i<j<ki < j < k and 2aj=ai+ak2a_j = a_i + a_k. Let nn be a positive integer. Show that the numbers 1,2,3,…,n1, 2, 3, \ldots, n can be reordered in a list that does not contain arithmetic trios.
number theoryrecursiveArithmetic Progression