MathDB

Let

a > b

be relatively prime positive integers. A grashopper stands at point

0

in a number line. Each minute, the grashopper jumps according to the following rules:
[*] If the current minute is a multiple of

a

and not a multiple of

b

, it jumps

a

units forward. [*] If the current minute is a multiple of

b

and not a multiple of

a

, it jumps

b

units backward. [*] If the current minute is both a multiple of

b

and a multiple of

a

, it jumps

a - b

units forward. [*] If the current minute is neither a multiple of

a

nor a multiple of

b

, it doesn't move.
Find all positions on the number line that the grasshopper will eventually reach.

Problem Statement