Properties
- It was shown in 2000 that the Kaprekar numbers for base b are in bijection with the unitary divisors of bn − 1, in the following sense. Let Inv(a,b) denote the multiplicative inverse of a modulo b, namely the least positive integer m such that . Then, a number X is in the set K(N) (defined above) if and only if X = d Inv(d, (N-1)/d) for some unitary divisor d of N-1. In particular,
- For each X in K(N), N - X is in K(N).
- In binary, all even perfect numbers are Kaprekar numbers.
Read more about this topic: Kaprekar Number
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