Dr Nilamoni Saikia

THE RELATIONSHIP BETWEEN PARTITION FUNCTION AND DIVISOR FUNCTION
P N Phukan1 and N Saikia2
Deptt. of Mathematical Sciences, Chaiduar College, Gohpur-784168 India
E-mail:nilamonisaikia@yahoo.com
Abstract:
The section move and the divisor course are two get theoretic portions in addition come up theory and increasing number theory respectively. The number theoretic answers play classical roles in number theory. In earlier studies many authors direct established relationships among some(a) of these functions, but not all of them. In this paper we establish relationship between partition function and divisor function along with some theorems related to from each one functions.
Kew words: partition function, divisor function, generating function, Ferrers diagram, pentagonal numbers.
PACS number: 03.65.Ge,o3.65.Fd,03.65.-w

1. ledger entry:
In multiplicative number theory we are implicated with how a autocratic whole number is constructed as a crossing of prime numbers or product of divisors. Two objects of lodge in here are the sum of divisors function ?(n) and number of divisors function d(n), which are , the sum of divisors and number of divisors of n respectively.



Additive number theory, on the other hand, is concerned with how a positive integer can be constructed as the sum of numbers from some set. The goal of this paper is to show the relationships between partition function and divisor function. In order to do that, one necessarily to describe these two functions which is the aim of this paper along with their properties. At first we define the respective function , illustrated with simple examples, undertaken problems, obtained generating functions for several(prenominal) partition functions, solve some theorems related to each function and then shows the relationships between the partition function and divisor function.

2. Partitions:
rendering 2.1:-
A partition of a non-negative integer n is a representation of n as a sum of positive integers. We often write the...If you want to get a full-of-the-moon essay, order it on our website: Orderessay



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