I don't have any specific problems I need help with, but I'm a bit confused about two things:

1) Where 2^x - 1 = y, is x or y the Mersenne prime?

2) I have noticed that in some cases, such as 27 * 3, I can break the problem up and arrive at the correct result:

27 * 3 = 81

(20 * 3) + (7 * 3) = 60 + 21 = 81

Does this work in all cases? I'm having trouble finding a problem that isn't correctly solved this way, but in the past I have tried this and arrived at the wrong answer. Does anyone know how this works?

2 answers

2) it works in all cases.

(a+b)c=a*c + b*c is why this is true.

1) y is the Mersenne Prime. And, big news in that area, the first 44 are now known.

http://www.mersenne.org/
I see, thanks. I must have been doing it wrong when it didn't work.