A property of the divisors of 99

by David Radcliffe

James Tanton (@jamestanton) asked an interesting question on Twitter. Which numbers have the property that the reverse of any multiple of them is again a multiple?

It turns out that the numbers with this property are exactly the divisors of 99 (1, 3, 11, 33, and 99). This property of the divisors of 99 is mentioned in the OEIS, but I have been unable to find a proof in the literature (by which I mean Google). To fill this gap, I have written my own proof, but you might wish to try your hand at proving it yourself.

Numbers that divide the reversals of their multiples