Let K be a number field of degree d and let a and b be comprime algebraic integers in K. The aim of the present paper is to refine A. Pinter's bound for the size of the integer solutions of elliptic equations in the rational case given in {On the magnitude of integer points on elliptic curves} (Bull. Austral. Math. Soc. 52 (1995), 195-199). In particular in this paper the author with the essential contribution of D. Poulakis presents an upper estimate for the size of the integer solutions of the specific elliptic equation y^2=x^3+ax+b depending only on the prime factors of the discriminant of the polynomial f(X)=X^3+aX+b and not on its height in the important case that a and b are coprime algebraic integers in arbitrary K. (The original result is given in section 2, Theorem 1).

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 43
Περίοδος	2000
Συγγραφέας	Yann Bugeaud
Αρ. Αρθρου	8
Σελίδες	125-130
Γλώσσα	-
Λέξεις Κλειδιά	elliptic equations, integer solutions, coprime algebraic integers

On the size of integer solutions of elliptic equations, II