IMO Shortlist 2006 problem N6

  Avg: 0,0
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
Let a > b > 1 be relatively prime positive integers. Define the weight of an integer c, denoted by w(c) to be the minimal possible value of |x| + |y| taken over all pairs of integers x and y such that ax + by = c. An integer c is called a local champion if w(c) \geq w(c \pm a) and w(c) \geq w(c \pm b). Find all local champions and determine their number.
Izvor: Međunarodna matematička olimpijada, shortlist 2006