Integral points on elliptic curves
Tom 67 / 2019
Bulletin Polish Acad. Sci. Math. 67 (2019), 53-67
MSC: Primary 11G05; Secondary 11D25, 11D45.
DOI: 10.4064/ba8152-1-2019
Opublikowany online: 28 March 2019
Streszczenie
We provide a description of the integral points on elliptic curves y^{2}=x(x- 2^{m}) \times (x+p), where p and p+2^{m} are primes. In particular, we show that for m=2 such a curve has no nontorsion integral point, and for m=1 it has at most one such point (with y \gt 0). Our proofs rely upon numerical computations and a variety of results on quartic and other diophantine equations, combined with an elementary analysis.
