29
International Journal of Algorithms, Computing and Mathematics
Volume 3, Number 4, November 2010
©Eashwar Publications
Nine Multifunction Number
Chandan Kumar, Anuj Agarwal, Munindra Kumar
Department of Civil Engineering,
Delhi College of Engineering, Bawana Road, Delhi – 42
India
chandankumardce@yahoo.co.in
Abstract
In the present paper, we are going to highlight and study the importance of nine as a
multifunction number. We hae developed two new functions and studied their
corresponding graph with reference to the above context.
Keywords: Mathematical Induction, functions, Number Systems, Graphs.
Introduction
The first function states that any number obtained by reversing the digits of the original
number, then the difference between the original number and the reversed number is an
integral multiple of nine.
The second function states that any number obtained by adding the digits of the original
number and the modified number is an integral multiple of nine.
−1
The statement expressed in the form of function would be given by:
Where,
C (n) = original number with n number of digits.
C (n) = number obtained after reversing the digits of original number.
K (n) = f [C (n)]
The statement expressed in the form of function would be given by:
(2)
K (n) = [C (n) − S (n)]
(3)
Where,
C (n) = original number with n number of digits.
S (n) = number obtained after adding the digits of original number.