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Problem 78

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Coin partitions

Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so p(5)=7.

OOOOO
OOOO O
OOO OO
OOO O O
OO OO O
OO O O O
O O O O O

Find the least value of n for which p(n) is divisible by one million.

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硬币分拆

记p(n)是将n枚硬币分拆成堆的不同方式数。例如，五枚硬币有7种分拆成堆的不同方式，因此p(5)=7。

OOOOO
OOOO O
OOO OO
OOO O O
OO OO O
OO O O O
O O O O O

找出使p(n)能被一百万整除的最小n值。

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