The aim of this article is to study the system piecewise linear difference equations xn+1=|xn|−yn−b and yn+1=xn−|yn|+1 where n≥0. A global behavior for b=4 shows that all solutions become equilibrium point. For a large value |x0| |y0|, we can prove (i) if b=5, then solution becomes point (ii) b≥6, periodic prime period 5.

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

Given a finite set of eigenvalues regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, potential q(x) which is unknown. We show possibility to compute more without any additional information on q(x). Moreover, considering with boundary conditions y{\prime}(0)-hy(0)=0 and y{\prime}({\pi})+Hy({\pi})=0, where h, H are some constants, we complete its spectrum neithe...

Public-key cryptography is rapidly becoming ubiquitous in many aspects of “electronic” life. It is used to provide various security services such as data integrity, confidentiality, authentication and nonrepudiation. Most public-key cryptographic methods require the generation of random prime numbers. A naive solution to obtain a prime number consists in randomly choosing a number and testing i...

The coefficients and the discriminant of the octic period polynomial i/^z) are computed, where, for a prime p = 8/ + 1, ^(r) denotes the minimal polynomial over Q of the period (1/%)2.%Z¡ exp(2trins/p). Also, the finite set of prime octic nonresidues (mod p) which divide integers represented by i|/8(z) is characterized.

We consider the minimal number of solutions to (n) = (n + k) for xed values of k. Previous work of A. Schinzel concerning this problem is described, as is the outcome of recent computational searches conducted to extend Schinzel's results. Let k be a xed positive integer. In this note, we consider the minimum number of solutions to the equation (n) = (n + k); (1) where n is a positive integer a...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.