Primitive elements and polynomials with arbitrary trace

Primitive Elements

Importantly, there is no element 1 ≤ k < p − 1 such that a ≡ 1(modp). The concepts presented in the study of primitive elements can be considered special cases of more general idea presented in group theory. Specifically, the primitve element a can be seen as a generator of Zp, we wil discuss this in more detail in the first section of the paper. Primitive elements also have applications in enc...

Trace Elements Status in Sera of Patients with Allergic Asthma

Background: Asthma is a multifactorial disease and its severity varies with the inflammatory grade. There are conflicting reports about the roles of trace elements in asthma. This study examined the effects of zinc (Zn), copper (Cu), and selenium (Se) concentrations in sera of patients with allergic asthma attending Ghaem Hospital, Mashhad, Iran. Methods: Forty-nine patients, aged 10 to 50 y...

Primitive Polynomials with Prescribed Second Coefficient

The Hansen-Mullen Primitivity Conjecture (HMPC) (1992) asserts that, with some (mostly obvious) exceptions, there exists a primitive polynomial of degree nover any finite fieldwith any coefficient arbitrarily prescribed. This has recently been provedwhenever n ≥ 9. It is also known to be true when n ≤ 3.We show that there exists a primitive polynomial of any degree n ≥ 4 over any finite field w...

Trace elements.

Trace Elements and Epidemiology.

In the one hundred years since the birthday of Academician W. J. Vernadsky, in whose honour this Geochemical Conference is being held, the population of our world has grown from about 1,250 million to not far short of 3,150 million, an addition of some 1,900 million persons. Thus, there are approximately two and one half times as many people in the world today as there were when Academician Ver...