Problem

Let b be a positive integer and let a be an integer with a four-digit base b expansion, wi...

Let b be a positive integer and let a be an integer with a four-digit base b expansion, with not all digits the same. Define Tb(a) = a′ − a″, where a′ is the integer with base b expansion obtained by writing the base b digits of a in ascending order.

Determine whether there is a Kaprekar constant for three-digit integers to the base 10. Prove that your answer is correct.

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