We give new bounds for the number of integral points on elliptic curves. The method may be
said to interpolate between approaches via diophantine techniques and methods based on …

Bibliography Page 1 Bibliography [1] Abel-Hollinger, CS, Zimmer, HG: Torsion groups of elliptic
curves with integral j-invariant over multiquadratic fields. In: Proceedings of the Int. Conf …

A set of m positive integers is called a Diophantine m-tuple if the product of its any two
distinct elements increased by 1 is a perfect square. We prove that if {a, b, c} is a …

In the first part we construct algorithms (over $\mathbb {Q} $) which we apply to solve $ S $-
unit, Mordell, cubic Thue, cubic Thue–Mahler and generalized Ramanujan–Nagell …

Diophantine m-tuples and elliptic curves Page 1 JOURNAL DE THÉORIE DES NOMBRES
DE BORDEAUX ANDREJ DUJELLA Diophantine m-tuples and elliptic curves Journal de …

Let the elliptic curve E be defined by the equationformula herewith a1,…, a6∈ ℤ. Define a
finite set of places S={q1,…, qs− 1, qs=∞} of ℚ and put Q= max {q1,…, qs− 1}. Let E (ℚ) …

This book presents in a unified and concrete way the beautiful and deep mathematics-both
theoretical and computational-on which the explicit solution of an elliptic Diophantine …

Landau's conjecture and Shanks' conjecture state that there are infinitely many prime
numbers of the forms x 2+ 1 and x 4+ 1 for some nonzero integer, respectively. In this paper …

We combine the method of Faltings (Arakelov, Paršin, Szpiro) with the Shimura–Taniyama
conjecture to prove effective finiteness results for integral points on moduli schemes of …

Cryptography is an evolving field that research into discreet mathematical equation that is
representable by computer algorithm for providing message confidentiality. The scheme has …