IMO 2006 Shortlist N6
Let a > b > 1 be relatively prime positive integers. Define the weight of an integer c, denoted by w(c), to be the minim...
Category: Number Theory
Problem
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) ≥ w(c ± a) and w(c) ≥ w(c ± b). Find all local champions and determine their number. (USA)