Let a∈ℤ and ρ be a root of f (x)=x 3 -ax 2 -(a+3)x-1, then the number field K =ℚ(ρ) is called simplest cubic field. In this paper we consider family unit equations u 1 +u =n where ,u ∈ℤ[ρ] * n∈ℤ. We completely solve under restriction |n|≤max{1,|a| 1/3 }.

Having considered the linear Stokes equations, we will now bring back the nonlinear term and consider the nonlinear version of the Stokes system. The solution of these equations can be viewed as the limit to which the solution of the full N-S equations tends as t tends to infinity. Of course no one knows at this point if the solutions of the N-S equations do tend to some limit as t tends to inf...

Aims: The aim of the research study was to develop a more direct and intuitive approach for solution polynomial equations degree 3 four.
 Study Design: employed equivalent substitution that is formulate than traditional formulations one easily solvable.
 Place Duration Study: has been undertaken by author at university Eswatini in period from February March 2021.
 Methodology: Tw...

The system of equations $$\begin{aligned}&u_1p_1^2 + \cdots u_sp_s^2 = 0,\\&v_1p_1^3 v_sp_s^3 0 \end{aligned}$$ has prime solutions $$(p_1, \ldots , p_s)$$ for $$s \ge 12$$ assuming that the modulo each p. This is proved via Hardy–Littlewood circle method, building on Wooley’s work corresponding over integers and recent results Vinogradov’s mean value theorem. Additionally, a set sufficient ...