This is in regard to proving that the statements (a) $\displaystyle a$ and $\displaystyle n$ are coprime and (c) row $\displaystyle a$ of the multiplication table for $\displaystyle Z_{n}$ includes all of $\displaystyle Z_{n}$

$\displaystyle ab = kn + 1$

"this equation implies that $\displaystyle a$ and $\displaystyle n$ are coprime because any common factor of $\displaystyle a$ and $\displaystyle n$ must also be a factor of 1

I don't see why this is so.