Title: The Łojasiewicz Exponent via The Valuative Hamburger-Noether Process,
Abstract: Let $k$ be an algebraically closed field of any characteristic. We apply the
Hamburger-Noether process of successive quadratic transformations to show the
equivalence of two definitions of the {\L}ojasiewicz exponent
$\mathfrak{L}(\mathfrak{a})$ of an ideal $\mathfrak{a}\subset k[[x,y]]$.