Divisors of zero in $ \mathbb Z_{p^k}$ Let $p$ be a prime numer and let $k$ be a natural numer such that $k\geq 2$. I wish to descripe all zero's divisors in $\mathbb Z_{p^k}$. Obviously elements of the form
$np$, where $n=0,...,p^{k-1}-1$, are zero divisors, because $p^k|np^k$.
Are there  others?

Suppose $ab=0$, and $p\nmid a$.  Well $p^k|ab$, so $p^k|b$, so $b=0$.  Hence you found them all.
