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In 1977 Hartwig and Luh asked whether an element 
$a$ in a Dedekind-finite ring 
$R$ satisfying 
$aR= {a}^{2} R$ also satisfies 
$Ra= R{a}^{2} $. In this paper, we answer this question in the negative. We also prove that if 
$a$ is an element of a Dedekind-finite exchange ring 
$R$ and 
$aR= {a}^{2} R$, then 
$Ra= R{a}^{2} $. This gives an easier proof of Dischinger’s theorem that left strongly 
$\pi $-regular rings are right strongly 
$\pi $-regular, when it is already known that 
$R$ is an exchange ring.
