Pseudo-random numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on “almost primitive” trinomials, that is trinomials ha...

We discuss the numbers in the title, and in particular whether the minimum period of the Bell numbers modulo a prime p can be a proper divisor of Np = (pp − 1)/(p− 1). It is known that the period always divides Np. The period is shown to equal Np for most primes p below 180. The investigation leads to interesting new results about the possible prime factors of Np. For example, we show that if p...

In this correspondence, it is shown that Legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2n elements, whenever p = 2n 1 is prime for some R 2 3.

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial xp−x−1 over Fp divides g(p) = p p−1 p−1 . Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1, . . . , g(p)} that do not contain o(r).

BACKGROUND In our study we compared the Ringer solution, which is the standard prime solution of our department, with the HES (Hydroxyethyl starch) 130-0.4 solution, which can be a potential alternative prime solution with an indispensable material for the cardio-pulmonary bypass applications. METHODS 140 patients undergoing to CABG (Coronary Artery Bypass Graft surgery) were electively enrol...

we prove the generalized hyers--ulam stability  of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.