On the Solutions to the Diophantine Equation

نویسنده

  • BRIAN PETERSON
چکیده

In this paper we are concerned with a question that has already been answered, involving Fibonacci-type sequences and their characteristic numbers. We are only interested in primitive sequences iconsecutive pairs of terms have no common factors) and for these sequences we ask: What numbers can be the characteristic of a sequence, and given such a number, how many sequences have it? Thoro [1] has shown that D may be the characteristic of a sequence if and only if Z7 has prime power decomposition D = 5°p?ip?* -C .

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Diophantine Equation x^6+ky^3=z^6+kw^3

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

متن کامل

Diophantine Equations Related with Linear Binary Recurrences

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

متن کامل

On Cornacchia’s algorithm for solving the diophantine equation

We give a new proof of the validity of Cornacchia’s algorithm for finding the primitive solutions (u, v) of the diophantine equation u + dv = m, where d and m are two coprime integers. This proof relies on diophantine approximation and an algorithmic solution of Thue’s problem.

متن کامل

On Pillai’s Diophantine equation

Let A, B, a, b and c be fixed nonzero integers. We prove several results on the number of solutions to Pillai’s Diophantine equation Aa −Bby = c in positive unknown integers x and y.

متن کامل

Short solutions for a linear Diophantine equation

It is known that finding the shortest solution for a linear Diophantine equation is a NP problem. In this paper we have devised a method, based upon the basis reduction algorithm, to obtain short solutions to a linear Diophantine equation. By this method we can obtain a short solution (not necessarily the shortest one) in a polynomial time. Numerical experiments show superiority to other method...

متن کامل

Upper Bounds for the Number of Solutions of a Diophantine Equation

We give upper bound estimates for the number of solutions of a certain diophantine equation. Our results can be applied to obtain new lower bound estimates for the L1-norm of certain exponential sums.

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010