Some diophantine equations involving arithmetic functions

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود 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

Diophantine Equations Involving Arithmetic Functions of Factorials

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:

متن کامل

Some Diophantine relations involving circular functions of rational angles

The eigenvalues of the 3 off-diagonal matrices of rank n with elements 1 + i cot [(j − k)π/n], sin[(j − k)π/n] and sin[(j − k)π/n], (j = 1, 2, . . . , n, k = 1, 2, . . . , n, j 6= k) are computed. The sums over k from 1 to n− 1 of cot (kπ/n) sin (2skπ/n) and sin(kπ/n)cos(2skπ/n) are moreover computed for s integer and p=2 and 4. The results are given by simple formulae in terms of integers. In ...

متن کامل

Equations Involving Arithmetic Functions of Fibonacci and Lucas Numbers

For any positive integer k, let (k) and a(k) be the number of positive integers less than or equal to k and relatively prime to k and the sum of divisors ofk, respectively. In [6] we have shown that 0(Fn) > F^n) and that a(Fn) < Fa{ri) and we have also determined all the cases in which the above inequalities become equalities. A more general inequality of this type was proved in [7]. In [8] ...

متن کامل

Diophantine Equations, Presburger Arithmetic and Finite Automata

We show that the use of nite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity.

متن کامل

On Some Diophantine Equations (i)

In this paper we study the equation m−n = py,where p is a prime natural number, p≥ 3. Using the above result, we study the equations x + 6pxy + py = z and the equations ck(x 4 + 6pxy + py) + 4pdk(x y + pxy) = z, where the prime number p ∈ {3, 7, 11, 19} and (ck, dk) is a solution of the Pell equation, either of the form c −pd = 1 or of the form c − pd = −1. I. Preliminaries. We recall some nece...

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: Journal of Mathematical Analysis and Applications

سال: 1966

ISSN: 0022-247X

DOI: 10.1016/0022-247x(66)90148-x