4
votes
0answers
108 views

Why limit Euler's Partition function P to $k\leq\sqrt n$ instead of $k\leq n$?

I solved a Project Euler problem (I won't say which one) involving the Partition Function P. I used equation #11 from the above link: $$P(n) = \sum_{k=1}^n (-1)^{k+1}\bigg(P\Big(n-{1\over ...
1
vote
1answer
261 views

How does $P(n)$ (Partition Function P) work?

I am trying to do Project Euler #78, which is about the different ways of splitting up coins into piles. I realized that this is just the number of integer partitions of the number of coins, ...