Consider an ndigit number k. Square it, and then add the right n digits to the left n or n1 digits (by convention, the second part may start with the digit 0, but must be nonzero). If the result is k then it is called a Kaprekar number. They are named after D. R. Kaprekar, a recreational mathematician from India.
We can extend the definition to any base b:
Let X be a nonnegative integer and n a positive integer. X is an nKaprekar number for base b if there exist nonnegative integer A, and positive integer B satisfying:
 X^{2} = Ab^{n} + B, where 0 < B < b^{n}
 X = A + B
Wikipedia
Examples in Base 10

297: 297^{2} = 88209, which can be split into 88 and 209, and 88 + 209 = 297.
 999: 999^{2} = 998001, which can be split into 998 and 001, and 998 + 001 = 999.
 In particular, 9, 99, 999… are all Kaprekar numbers.
 More generally, for any base b, there exist infinitely many Kaprekar numbers, including all numbers of the form b^{n} − 1.

100: 100 is NOT a Kaprekar number as, although 100^{2} = 10000 and 100 + 00 = 100, the second part here is zero.
M x
(P.S. Another post on Kaprekar is coming soon!)