Definition
Let X be a non-negative integer. X is a Kaprekar number for base b if there exist non-negative integers n, A, and positive number B satisfying:
- X² = Abn + B, where 0 < B < bn
- X = A + B
Note that X is also a Kaprekar number for base bn, for this specific choice of n. More narrowly, we can define the set K(N) for a given integer N as the set of integers X for which
- X² = AN + B, where 0 < B < N
- X = A + B
Each Kaprekar number X for base b is then counted in one of the sets K(b), K(b²), K(b³),….
Read more about this topic: Kaprekar Number
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