Show that if a and b are positive integers, then there is a smallest positive integer of the form $a - bk, \ k \in \mathbb{Z}$.
Show that if a and b are positive integers, then there is a smallest positive integer of the form $a - bk, \ k \in \mathbb{Z}$.
Consider the set, $S = \{a-bk > 0 | k \in \mathbb{Z} \}$