文摘
Büchis problem asks if there exists a positive integer M such that all satisfying the equations for all 3rM must also satisfy for some integer x. Hensleys problem asks if there exists a positive integer M such that, for any integers ν and a, if (ν+r)2−a is a square for 1rM, then a=0. It is not difficult to see that a positive answer to Hensleys problem implies a positive answer to Büchis problem. One can ask a more general version of the Hensleys problem by replacing the square by n-th power for any integer n2 which is called the Hensleys n-th power problem. In this paper we will solve Hensleys n-th power problem for complex meromorphic functions and non-Archimedean meromorphic functions.