  We study totally positive, additively indecomposable integers in a real
quadratic field $\mathbb Q(\sqrt D)$. We estimate the size of the norm of an
indecomposable integer by expressing it as a power series in $u_i^{-1}$, where
$\sqrt D$ has the periodic continued fraction expansion $[u_0, u_1, u_2, \dots,
u_{s-1}, 2u_0, u_1, u_2, \dots]$. This enables us to disprove a conjecture of
Jang-Kim [JK] concerning the maximal size of the norm of an indecomposable
integer.

Number Theory