Problem

Source: Bulgarian Autumn Tournament 2023, 11.1

Tags: algebra



A quadruplet of distinct positive integers (a,b,c,d) is called k-good if the following conditions hold: 1. Among a,b,c,d, no three form an arithmetic progression. 2. Among a+b,a+c,a+d,b+c,b+d,c+d, there are k of them, forming an arithmetic progression. a) Find a 4-good quadruplet. b) What is the maximal k, such that there is a k-good quadruplet?