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four numbers two deleted and replaced with a+b and ab

Source: Azerbaijan EGMO TST 2017, D2 P2

July 31, 2023
combinatorics

Problem Statement

Four numbers are written on the board: 1,3,6,10.1, 3, 6, 10. Each time two arbitrary numbers, aa and bb are deleted, and numbers a+ba + b and abab are written in their place. Is it possible to get numbers 2015,2016,2017,20182015, 2016, 2017, 2018 on the board after several such operations?
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