Abstract
We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if <TEX>$P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$</TEX>, where <TEX>$f_1,{\ldots},f_{N+1}$</TEX>; <TEX>$g_1,{\ldots},g_{N+1}$</TEX> are two families of linearly independent entire functions, then <TEX>$f_i=cg_i$</TEX>, <TEX>$i=1,2,{\ldots},N+1$</TEX>, 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.
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