TITLE: How to prove Euler's pentagonal theorem? Some hints will help
QUESTION [11 upvotes]: Euler's pentagonal theorem is the following equation:
    $\prod\limits_{n=1}^{+\infty}(1-q^n)=\sum\limits_{m=-\infty}^{+\infty}(-1)^m q^{\frac{3m^2-m}{2}}$
where $|q|<1$ is a complex number.
I hope that someone will me some hints on this.

REPLY [3 votes]: There are two other proofs you might like: Andrews's proof of Jacobi triple product identity  which implies Euler's Pentagonal Theorem, and has a direct bijective proof given by Sylvester (see my survey.   
Another, quite different proof is due to Dyson and given here (see my survey and this popular article explaining the connection).