Shexi Chen, Zhigang Li
Abstract
In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x4 − 4sx3 y + (12s − 4)x2 y2 − 8sxy3 + 4y4 = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).
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In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x4 − 4sx3 y + (12s − 4)x2 y2 − 8sxy3 + 4y4 = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).
Key concepts: Parameterized complexity, Quartic function, Thue equation, Mathematics, Quartic surface, Discrete mathematics, Pure mathematics, Combinatorics