MathDB

Let

a, b

be two co-prime positive integers. A number is called good if it can be written in the form

ax + by

for non-negative integers

x, y

. Define the function

f : Z\to Z

f(n) = n - n_a - n_b

, where

s_t

represents the remainder of

s

upon division by

t

. Show that an integer

n

is good if and only if the infinite sequence

n, f(n), f(f(n)), ...

contains only non-negative integers.

Problem Statement