A few days ago, there was a thread where it was asked if you could solve it for c == 2 (aka squares). You participated in the thread, so you should know that noone proved it possible, and the general feeling was that it is impossible for squares.

I would focus on solving the square question before asking the more general question.

Having said that, there's a trivial answer: /^/ - which always matches. As there are always a b and a c: b == $number and c == 1. But I guess you aren't interested in that.