Preprint of "On Integers Whose Sum is the Reverse of their Product" available on the arXiv

 

The preprint of "On Integers Whose Sum is the Reverse of their Product", feat. Xander Faber is now available on the math arXiv.

Have you ever noticed that 9+9=18, while 9x9=81, which is 18 backwards? My co-author's kids did. The question of what other pairs of numbers a and b have a+b equal to axb backwards led us to write this paper. We give a technique for solving it in all bases. We have seen a list of these numbers in base 10 on the web, but we are aware of no other proof.