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Let $p_0^d (n)$ be the number of partitions of n into distinct odd parts. Show that $$p(n) \equiv p_0^d(n) \pmod 2$$

So I have to show that the total number of partitions has the same parity as the number of partitions of n into distinct odd parts. I know that there are equal amounts of even and odd partitions, but other than that don't really know how to approach this.

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    If you want to find out about ideas and tools for treating problems about integer partitions, the book Integer Partitions by G. Andrews and K. Eriksson, (Cambridge U. Press, 2004) is a very nice account.2011-04-28
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    This is really an aside, but anyways, here professor Ken Ono talking about integer partitions in a popularized talk http://www.youtube.com/watch?v=aj4FozCSg8g2011-04-28

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