The Power And The Sequence Of Binomial Coefficients Of Congruence Nature And Applications

Binomial coefficient is an important research issue of the number theory, especially is a powerful tool in searching and proving irrational numbers.In this thesis, some congruence properties of binomial coefficient sequences are obtained, and furthermore a lower bound for the minimal length of the polynomial recurrence of a binomial sum is achieved.The main contents of this thesis are as follows:The first chapter briefs the origin, the background, the development of binomial coefficient sequence and the main content of the thesis.The second chapter introduces divisibility and congruence theory and other related theory.The third chapter proves the congruence properties of some binomial coef-ficient sequences.The forth chapter proves two theorems as follows:Considering the sequencesa lower bound for the minimal length of the recurrence is obtained by using the properties of congruence.