论文信息 - Solving constrained Pell equations

Solving constrained Pell equations

Consider the system of Diophantine equations x 2 - ay 2 = b, P(x, y) = z 2 , where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker's method to produce an upper bound on the integer solutions. We present a general elementary approach, based on an idea of Cohn and the theory of the Pell equation, that solves many such systems. We apply the approach to the cases P(x, y) = cy 2 + d and P(x, y) = cx + d, which arise when looking for integer points on an elliptic curve with a rational 2-torsion point.

Kiran S. Kedlaya

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