JP Journal of Algebra, Number Theory and Applications
Volume 47, Issue 2, Pages 135 - 155
(August 2020) http://dx.doi.org/10.17654/NT047020135 |
|
ON A VARIANT OF KAPREKAR NUMBERS – MINUS-KAPREKAR NUMBERS
Atsushi Yamagami and Vidhi Mukund Ketkar
|
Abstract: Let and be any integers. It is well-known that a positive integer X is called an n-Kaprekar number in the base b if there exist integers such that and For example, 45 is a 2-Kaprekar number in the base 10, since and In this article, we give the definition of a variant of Kaprekar numbers. Namely, we call a positive integer x “an n-minus-Kaprekar number in the base b” if there exist positive integers A, B with such that and For example, 1078 is a 3-minus-Kaprekar number in the base 10, since and Then we see a characterization of minus-Kaprekar numbers and how to construct them. Moreover, as an appendix, we see a brief survey of Iannucci’s result on Kaprekar numbers and its application which includes a new viewpoint of characterizations of Mersenne prime numbers. |
Keywords and phrases: Kaprekar numbers, Mersenne prime numbers.
|
|
Number of Downloads: 228 | Number of Views: 706 |
|