Affiliation:
1. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2, Canada
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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1. Integral points on the elliptic curve $y^2=x^3-4p^2x$;Czechoslovak Mathematical Journal;2019-03-26
2. On certain Diophantine equations of the form z2=f(x)2±g(y)2;Journal of Number Theory;2017-05
3. Shifted powers in binary recurrence sequences;Mathematical Proceedings of the Cambridge Philosophical Society;2015-01-08