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We will use Thue-Siegel method, based on Pad\'e approximation viahypergeometric functions, to give upper bounds for the number of integralsolutions to the equation $|F(x, y)| = 1$ as well as the inequalities $|F(x,y)| \leq h$, for a certain family of irreducible quartic binary forms.

The Method Of Thue-Siegel For Binary Quartic Forms