Solving a family of quartic Thue inequalities using continued fractions
نویسندگان
چکیده
In this paper we find all primitive solutions of Thue inequality |x4 + 2(1− n)xy + y4| ≤ 2n + 3, where n ≥ 3 is an integer.
منابع مشابه
Solutions of a class of quartic Thue inequalities
Let c be a positive integer. In this paper, we use the method of Tzanakis to transform the quartic Thue inequality |x − 4xy − (2c− 2)xy + (4c+ 4)xy − (2c− 1)y| ≤ max { c 4 , 4 } into systems of Pellian equations. Then we find all primitive solutions of this inequality using continued fractions.
متن کاملA 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 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 کاملTo appear in J. Symbolic Comput. ALL SOLUTIONS TO THOMAS’ FAMILY OF THUE EQUATIONS OVER IMAGINARY QUADRATIC NUMBER FIELDS
We completely solve the family of relative Thue equations x − (t − 1)xy − (t+ 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t| ≥ 53 and Baker’s method combined with a computer search using continued fractions for the remaining values of t.
متن کاملAll solutions to Thomas' family of Thue equations over imaginary quadratic number fields
We completely solve the family of relative Thue equations x − (t − 1)xy − (t + 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t| ≥ 53 and Baker’s method combined with a computer search using continued fractions for the remaining values of t.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008