Explicit estimates of solutions of some Diophantine equations
نویسندگان
چکیده
منابع مشابه
Parametric solutions for some Diophantine equations
Under some hypotheses we show that the Diophantine equation (1) has infinitely many solutions described by a family depending on k + 2 parameters. Some applications of the main result are given and some special equations are studied.
متن کاملPositive Solutions to Some Systems of Diophantine Equations
We consider a sequence defined by the number of positive solutions to a sequence of systems of Diophantine equations. We derive some bounds on the solutions to demonstrate that the terms of the sequence are finite. We develop an algorithm for 1 computing an arbitrary term of the sequence, and consider a graph-theoretic approach to computing the same.
متن کاملA Numerical Bound for Baker's Constant - Some Explicit Estimates for Small Prime Solutions of Linear Equations
proved that there is an absolute constant V > 0 such that the linear equation a 1 p 1 + a 2 p 2 + a 3 p 3 = b has prime solutions p j 's if b (max j a j) V and a j > 0. Apart from the numerical value of V , the bound is sharp. In this manuscript, we obtain a numerical bound for V. We also obtain a numerical bound for the small prime solutions of the above equation if the a j 's are not all of t...
متن کاملNew explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method
To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...
متن کاملThe Number of Solutions of Diophantine Equations
0. Introduction. In two recent papers 4], 30], Erdd os, Stewart and the author showed that certain diophantine equations have many solutions. In this way they indicated how far certain results are capable for improvements at most. First we mention some relevant results from the literature on upper bounds for the numbers of solutions of diophantine equations and then we sketch how our method lea...
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: Functiones et Approximatio Commentarii Mathematici
سال: 2008
ISSN: 0208-6573
DOI: 10.7169/facm/1229696538