The Study On The Finite Sum Of The Elementary Formulas For The Number Of Positive Integer Partitions

In this paper, we will give various exact formulas on integer partitions. Including thefunction of p(n) , p(n, k) and the function of p(n, k, l) . The function of p(n) is thenumber of partitions of n , the function of p(n, k) is the number of partitions of n intoexactly k parts, and the function of p(n, k, l) is the number of partitions of n intoexactly k parts the biggest of which is l. In this paper, we give the exact proof to theelementary formulas for integer partitions. Finally, we obtain the elementary formulas ofThe thesis is divided into three chapters:Chapter 1, we introduce the development of the Number Theory, and explain theimportance of integer partitions in theory and practice.Chapter 2, We give some symbols, definitions. In order to prove the main result, wegive the various exact elementary formulas, lemmas, and the exact proof.Chapter 3, we prove the main result of this thesis with the method of finite sum.Finally, we obtain the elementary formulas of p(n).