Bulletin of the
Korean Mathematical Society BKMS

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial $P$ of this class, if $P( f_1, \ldots ,f_{N+1})$ $ = P( g_1, \ldots ,g_{N+1})$, where $f_1, \ldots ,f_{N+1};$ $g_1, \ldots ,g_{N+1}$ are two families of linearly independent entire functions, then $f_i = cg_i, \ i=1, 2, \ldots , N+1,$ where $c$ is a root of unity. As a consequence, we prove that if $X$ is a hypersurface defined by a homogeneous polynomial in this class, then $X$ is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

Keywords: Diophantine equations, non-Archimedean field, unique range sets, holomorphic curves

MSC numbers: 11D88, 30D35