How to explicitly solve a Thue-Mahler equation

N. Tzanakis; B. M. M. de Weger

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Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

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We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.