Kaprekar number

Let n be a k-digit integer in base b. Then n is said to be a Kaprekar number in base b if n2 has the following property: when you add the number formed by its right hand digits to that formed by its left hand digits, you get n.

Or to put it algebraically, an integer n such that in a given base b has


(where dx are digits, with d0 the least significant digit and dk-1 the most significant) such that


if k is even or


if k is odd.

bx-1 for a natural x is always a Kaprekar number in base b.


  • 1 D. R. Kaprekar, “On Kaprekar numbers” J. Rec. Math. 13 (1980-1981), 81 - 82.
Title Kaprekar number
Canonical name KaprekarNumber
Date of creation 2013-03-22 16:00:17
Last modified on 2013-03-22 16:00:17
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63