Generalization Of Lucas Theorem About Congruence Of Binomial Coefficients

The research of congruence of binomial coefficients is one of the most important problems in combinatorial number theory. A beautiful theorem of Lucas states the congruence of binomial coefficients. Recently, there have been many articles on Lucas's theorem and its generalizations. Many examples of congruences related to the Lucas property of functions have occurred in the literature. For example, Apery numbers, Delannoy numbers and multinomial coefficients.In this thesis we investigate a class of functions satisfying similar congruences.The first of which introduces the congruence of binomial coefficients. We state the Legendre theorem, Kummer theorem and Lucas theorem.In the second chapter we present some sufficient conditions and more examples of Lucas functions. Some of which simplify the complex proofs.The third chapter introduces the self-similar structure and the distribution of the Pascal triangle and Lucas triangle.The fourth chapter mainly discusses the other problems of Lucas function.