Multivariable Intersective Polynomials

A polynomial f(x)with integer coefficient is called a intersective polynomial if f(x)=0 has no solution in Z,but f(x)= 0(mod m)has a solution for all integer m.Intersective polynomials are of importance in number theory and there are many important applica-tions in additive number theory and other fields.In this thesis,we shall determine a polynomial whether it is a intersective polynomial based on Hensel's lemma and the Chinese Remainder Theorem.Our first result in this thesis is that a polynomial with one degree can not be intersective polynomial.We give sufficient conditions to guarnomial a binary qudratic integer with coefficient polynomial is an intersective polynomial.We also determine a.binary polynomial is an intersective polynomial for degree greater than 2.The above results provide methods and ideas for furtuer research on multivariate polynomials.The research results of this paper play an important role in the development of additive number theory,algebraic number theory and other fields,and is of importance in analytic number theory.