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S -integral points on elliptic curves - Notes on a paper of B. M. M. de Weger

Emanuel Herrmann, Attila Pethö (2001)

Journal de théorie des nombres de Bordeaux

In this paper we give a much shorter proof for a result of B.M.M de Weger. For this purpose we use the theory of linear forms in complex and p -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.

Searching for Diophantine quintuples

Mihai Cipu, Tim Trudgian (2016)

Acta Arithmetica

We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most 5 . 441 · 10 26 Diophantine quintuples.

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