Puzzle time!

5 monkeys gather a pile of N peaches.  They agree to divide the peaches the following day.  Monkey A wakes up before the others, and wants some peaches, so he divides the peaches up evenly.  There's a leftover peach, so he rewards himself for his efforts.  He takes his share and leaves.  A gust of wind then combines the remaining 4 piles into 1.  Monkey B wakes up, and not knowing of A's actions, proceeds to do the same thing.  The same happens for the other 3 monkeys.  There are Q peaches after the final monkey takes his share.

Assuming no fractional peaches are involved, what is the smallest value of N, and the corresponding value of Q?  If you did this problem in a certain way, you should have an entire set of possible values of N and Q.

Obviously, this problem can be brute forced in various ways.  There is however, a quick and elegant solution.  In fact, this solution generalizes to K monkeys.  Can you find it?

>>13
>``N = 1 mod 5'' means ``N equals 1 modulo 5'', which is 1.
a) typing the congruent sign is non trivial
b) this meaning you're suggesting is almost non sense (unless you're speaking in terms of CS, but they use % for taking remainders), and I have never seen such a use in mathematical discussions
c) as a consequence of a and b, his meaning was obvious