Diophantine Equation With Mixed Powers And Prime Variables

Diophantine equations are equations(or system of equations)in which the number of unknowns is greater than the number of equations(or system of equations).Its solutions are integer solutions,rational solutions or other solutions with restrictions.Many scholars have obtained many good results in the process of studying Diophantine equation with mixed powers and prime variables.One of the important research topics of this kind of equations is the study of the exceptional sets of equations.For many problems in number theory,we can approach the desired result by decreasing the exceptional sets.In this paper,we study the representation of positive odd number n as (?) and obtain the corresponding exceptional set.In this paper,the circle method in additive number theory is used.The iterative method in circle method is used to deal with the major arcs and the exponential sum method is used to deal with the minor arcs.This paper concludes that:Theorem 1 ForLet N be a sufficiently large positive integer,(?)，then...