Study On The Related Problems Of Genocchi Numbers And Their Polynomials

In the world of number theory, the arithmetic functions and the related properties of polynomials are eternal topics, which have attracted generations of experts and scholars for learning and exploring. For instance, Bernoulli Numbers and Bernoulli polynomials, Euler Numbers and Euler polynomials, Fibonacci Numbers and Fibonacci polynomials and so on, their generalized types were also discussed.In this paper, based on the classic series, we studied the power series expan-sion of tangent and the properties of Genocchi numbers in elementary method, some relevant conclusions are obtained. Further, the determinant of Genocchi polynomial is given.The main contents are as follows:1. By using the method of comparing coefficient, the relation between the coefficient of power series and the Genocchi numbers was established. In addition, some identities and congruence expressions were obtained.2. The determinant of Genocchi polynomial is given through the Kramer law.3. Some identities of the integral polynomials of Genocchi polynomial are introduced with the method of generating function.