Let p be an odd prime and m be a positive integer. In this paper, we prove that the one-error linear complexity over Fp of Sidelnikov sequences of length p − 1 is ( p+1 2 ) − 1, which is much less than its (zero-error) linear complexity.

We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).

In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem { −Δpu+ a(x)up−1 = −u in Ω, |∇u|p−2 ∂u ∂ν = λup−1 on ∂Ω for λ ∈ R, where r > p − 1 > 0, a ∈ L∞(Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determine their asymptotic behavior both when r → p− 1 and when r → ∞.

We prove that if (x, y, n, q) 6= (18, 7, 3, 3) is a solution of the Diophantine equation (xn−1)/(x−1) = y with q prime, then there exists a prime number p such that p divides x and q divides p − 1. This allows us to solve completely this Diophantine equation for infinitely many values of x. The proofs require several different methods in diophantine approximation together with some heavy comput...

Background: The aim of this study was to evaluate seminal plasma coenzyme Q10 levels and oxidative stress in patients with different types of male infertility. Materials and Methods: The study took place in the Department of Chemistry and Biochemistry, College of Medicine, Al-Nahrain University- Baghdad-Iraq from the period of November 2004 till July 2006. Sixty patients with male infertility w...

On primitive roots of 1 mod p k , divisors of p ± 1, Wieferich primes, and quadratic analysis mod p Abstract Primitive roots of 1 mod p k (k >2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p+...

Cognitive abilities rise steeply from infancy to young adulthood and then are either maintained or decline to old age, depending on the specific ability. This pattern suggests corresponding continuities of mechanism and process, but it is striking that the fields of cognitive development and cognitive aging make little contact with each other's methods and theories. In this review we examine re...