Show that if a and b are positive integers, then there is a smallest positive integer of the form $\displaystyle a - bk, \ k \in \mathbb{Z}$.
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Originally Posted by Aryth Show that if a and b are positive integers, then there is a smallest positive integer of the form $\displaystyle a - bk, \ k \in \mathbb{Z}$. Consider the set, $\displaystyle S = \{a-bk > 0 | k \in \mathbb{Z} \}$ Argue that the set is non-empty and choose the smallest such natural number.
That was too easy, but my professor is a very nervous person and refuses to teach... Instead all of his lectures consist of the words "Uhh" and "Umm".
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