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In this article, we use Pad\'{e} approximations constructed for binomialfunctions, to give a new upper bound for the number of the solutions of the$S$-unit equation. Combining explicit formulae of these Pad\'{e} approximantswith a simple argument relying on Mahler measure and on the local height, werefine the bound due to J.-H. Evertse.

$S$-unit equation in two variables and Pad\'{e} approximations