Diophantine Equations Involving Arithmetic Functions of Factorials

نویسندگان

  • Daniel M. Baczkowski
  • Reza Akhtar
  • Patrick Dowling
  • Thomas Farmer
چکیده

DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation:

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

Equations Involving Arithmetic Functions of Factorials Ecuaciones que Involucran Funciones Aritméticas de Factoriales

For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum function of k, and the number of divisors of k, respectively. Let f be any of the functions φ, σ, or τ . In this note, we show that if a is any positive real number then the diophantine equation f(n!) = am! has only finitely many solutions (m,n). We also find all solutions of the above equation when ...

متن کامل

Univalent holomorphic functions with fixed finitely many coefficients involving Salagean operator

By using generalized Salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. Coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

متن کامل

Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms

The study of equations over the integers or the rational numbers is the subject of diophantine geometry. This also includes generalizations to finite extensions of the rationals, their rings of integers, and also to function fields over a finite field, and the rings of polynomials therein. This is a vast subject, in which a variety of methods from geometry, analysis, and arithmetic are used. Fo...

متن کامل

Self-similar fractals and arithmetic dynamics

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

متن کامل

Division by zero

For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably unsolvable in Robinson’s arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophanti...

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 2005