Integral points on elliptic curves y2 = x(x - 2m)(x + p)

• Autorzy: Jędrzejak Tomasz , Wieczorek Małgorzata

Identyfikatory

DOI

10.4064/ba8152-1-2019

• Języki publikacji: EN

Abstrakty

EN

We provide a description of the integral points on elliptic curves y² = x(x-2^m) x (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 > 0). Our proofs rely upon numerical computations and a variety of results on quartic and other diophantine equations, combined with an elementary analysis.

Słowa kluczowe

EN

elliptic curves; integral points; rank of elliptic curves; system of Pell equations; Thue equations

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 1
• Strony: 53--67
• Opis fizyczny: Bibliogr. 21 poz., tab.

Twórcy

autor

Jędrzejak Tomasz

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

autor

Wieczorek Małgorzata

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).