Solution of certain Pell equations

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Simultaneous Pell equations

Let R and S be positive integers with R < S. We shall call the simultaneous Diophantine equations x −Ry = 1, z − Sy = 1 simultaneous Pell equations in R and S. Each such pair has the trivial solution (1, 0, 1) but some pairs have nontrivial solutions too. For example, if R = 11 and S = 56, then (199, 60, 449) is a solution. Using theorems due to Baker, Davenport, and Waldschmidt, it is possible...

متن کامل

Solving constrained Pell equations

Consider the system of Diophantine equations x2 − ay2 = b, P (x, y) = z2, where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s method to produce an upper bound on the integer solutions. We present a general elementary approach, based on an idea of Cohn and the theory of the Pell equation, that solves many such systems. We apply the approach to th...

متن کامل

#A15 INTEGERS 12A (2012): John Selfridge Memorial Issue EXPLICIT SOLUTIONS OF CERTAIN SYSTEMS OF PELL EQUATIONS

We show how to obtain the solutions of families of systems of two Pell equations; these families are parameterized by the prime numbers. -Dedicated to the memory of John Selfridge. His opera voice is no more, but his voice in mathematics will continue to be heard, powerful.

متن کامل

Arithmetic Progressions on Pell Equations

IF Introduction sn IWWW fremner ‘I“ ™onsidered —rithmeti™ progressions on ellipti™ ™urvesF fremner ™onstru™ted ellipti™ ™urves with —rithmeti™ progressions of length UD iFeF r—tion—l points @X; Y A whose XE ™oordin—tes —re in —rithmeti™ progressionF sn — following p—per fremnerD ƒilverm—n —nd „z—n—kis ‘P“ showed th—t — su˜group of the ellipti™ ™urve E@QA with E X Y 2 a X@X 2 n 2 A of r—nk I doe...

متن کامل

On the resolution of simultaneous Pell equations ∗

We descibe an alternative procedure for solving automatically simultaneous Pell equations with relatively small coefficients. The word “automatically” means to indicate that the algorithm can be implemented in Magma. Numerous famous examples are verified and a new theorem is proved by running simply the corresponding Magma procedure requires only the six coefficients of the system a1x 2 + b1y 2...

متن کامل

ذخیره 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: Asian-European Journal of Mathematics

سال: 2018

ISSN: 1793-5571,1793-7183

DOI: 10.1142/s1793557118500560