# An analogue of mason's theorem for p-adic entire functions in several variables

1 Introduction Mason [7], [8] started one recent trend of thoughts by discovering an entirely new relation among polynomials as follows. Let f(z) be a polynomial with coefficients in an algebraically closed field of characteristic 0 and let nf be the number of distinct zeros of f. Then we have the following. Theorem A. (Mason Theorem,[4]). Let a(z), b(z), c(z) be relatively prime polynomials in k and not al l constants such that a + b = c. Then max{deg(a), deg(b), deg(c)} ≤ nabc − 1. Influenced by Mason's theorem, and considerations of Szpiro and Frey, Masser and Oesterle formulated the abc" conjecture ( see [4]).In [4], Hu and Yang shows that analogue of Theorem A for one variable non- Archimedean holomorphic functions is true.In this paper we proved a similar result of Theorem A for p−adic entire functions in several variables.

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