 Back
Research Article
ScienceAsia 27 (2001) : 133-136 |doi: 10.2306/scienceasia1513-1874.2001.27.133
Some Properties of the Kaprekar Numbers and a Means of Generation
Colin G Black*
ABSTRACT: This note describes what is believed to be a novel and easily implemented method for
generating integer Kaprekar numbers. The starting point for the method is the observation made here,
that a necessary condition for an integer k to be a Kaprekar number is that k must be congruent to k2
modulo-9. Moreover, it is also shown here that a Kaprekar number k is either a member of the residue
class [0] or residue class [1] modulo-9. For an integer k congruent to k2 modulo-9, further steps are
then established to find any integer values: q, r and n, such that k = q + r, and k2 = q x 10n + r. The
method described here is implemented using the computer algebra software package: Mathcad. A list of
the entire integer Kaprekar numbers lying between 1 and 106 is generated. In addition, some results
relating to the properties of the Kaprekar numbers are also presented.
Download PDF
Mechanical Engineering Program, Sirindhorn International Institute of Technology at Thammasat University, Pathum Thani 12121, Thailand.
* Corresponding author, E-mail: bcg@siit.tu.ac.th
Received 31 Jul 2000, Accepted 26 Jan 2001
|
