MathDB

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| \plus{} |y| taken over all pairs of integers

x

and

y

such that ax \plus{} by \equal{} 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.
Proposed by Zoran Sunic, USA

Problem Statement