منابع مشابه
A parametric family of quartic Thue equations
In this paper we prove that the Diophantine equation x − 4cxy + (6c+ 2)xy + 4cxy + y = 1, where c ≥ 3 is an integer, has only the trivial solutions (±1, 0), (0,±1). Using the method of Tzanakis, we show that solving this quartic Thue equation reduces to solving the system of Pellian equations (2c+ 1)U − 2cV 2 = 1, (c− 2)U − cZ = −2, and we prove that all solutions of this system are given by (U...
متن کاملOn two-parametric family of quartic Thue equations
We show that for all integers m and n there are no non-trivial solutions of Thue equation x − 2mnxy + 2 ( m − n + 1 ) xy + 2mnxy + y = 1, satisfying the additional condition gcd(xy,mn) = 1.
متن کاملExplicit solution of a class of quartic Thue equations
1. Introduction. In this paper we deal with the efficient solution of a certain interesting class of quartic Thue equations. In recent years general powerful methods have been developed for the explicit solution of Thue equations; see e.g. [TW], [PS] and the references given there. As these methods depend on rather heavy numerical computations, we think that methods for the solution of special ...
متن کاملOn the solutions of a family of quartic Thue equations
In this paper, we solve a certain family of diophantine equations associated with a family of cyclic quartic number fields. In fact, we prove that for n ≤ 5× 106 and n ≥ N = 1.191× 1019, with n, n+ 2, n2 + 4 square-free, the Thue equation Φn(x, y) = x 4 − nxy − (n + 2n + 4n+ 2)xy − nxy + y = 1 has no integral solution except the trivial ones: (1, 0), (−1, 0), (0, 1), (0,−1).
متن کاملA family of quartic Thue inequalities
In this paper we prove that the only primitive solutions of the Thue inequality |x − 4cxy + (6c + 2)xy + 4cxy + y| ≤ 6c + 4, where c ≥ 4 is an integer, are (x, y) = (±1, 0), (0,±1), (1,±1), (−1,±1), (±1,∓2), (±2,±1).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2010
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.07.010