07 July 2011

A cute number theory puzzle

Today's MAA number of the day, when multiplied by its successor, gives a number concatenated with itself. (Like 455 * 539 = 245245, except 539 isn't the successor of 455.)

Puzzle: find all such three-digit numbers. (The fact that I'm phrasing it this way should indicate to you that there's more than one.)

Meta-puzzle: generalize this. (I have some generalizations in mind.)