The difference between any number and another formed by reversing its digits has certain interesting properties, which, I believe, have not been explicitly noticed before, and these properties determine the necessary and sufficient conditions that a number may be expressed as such a difference.

To begin with, let us take a number having an even number of digits and denote it by

where a p , b p are the middle digits, b 1 the units digit and a 1>b 1.