Integral points on congruent number curves
نویسنده
چکیده
We provide a precise description of the integer points on elliptic curves of the shape y2 = x3 − N2x, where N = 2apb for prime p. By way of example, if p ≡ ±3 (mod 8) and p > 29, we show that all such points necessarily have y = 0. Our proofs rely upon lower bounds for linear forms in logarithms, a variety of old and new results on quartic and other Diophantine equations, and a large amount of (non-trivial) computation.
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تاریخ انتشار 2013