Function solutions to certain Diophantine equationsстатья
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Дата последнего поиска статьи во внешних источниках: 8 января 2017 г.
Аннотация:We investigate whether certain Diophantine equations have or have not solutions in entire or meromorphic functions defined on a non-Archimedean algebraically closed field of characteristic zero. We prove that there are no non-constant meromorphic functions solving the Erdős–Selfridge equation except when the corresponding curve is a conic. We also show that there are infinitely many non-constant entire solutions to the Markoff–Hurwitz equation.