  We prove that a simple knot in the lens space $L(p,q)$ fibers if and only if
its order in homology does not divide any remainder occurring in the Euclidean
algorithm applied to the pair $(p,q)$. One corollary is that if $p=m^2$ is a
perfect square, then any simple knot of order $m$ fibers, answering a question
of Cebanu. More generally, we compute the leading coefficient of the Alexander
polynomial of a simple knot, and we describe how to construct a minimum
complexity Seifert surface for one. The methods are direct, combinatorial, and
geometric.
