Abstract
In this paper we prove that the Diophantine equation x 4 4cx 3 y + (6c + 2)x 2 y 2 + 4cxy 3 + y 4 = 1, where c 3 is an integer, has only the trivial solutions (±1,0), (0,±1). Using the method of Tzanakis, we show that solving this quartic Thue equation reduces to solving the system of Pellian equations (2c + 1)U 2 2cV 2 = 1, (c 2)U 2 cZ 2 = 2,
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