Evaluate the following sum
\(\displaystyle\sum_{m=1}^\infty \sum_{\substack{n\ge 1\\ (m,n)=1}} \frac{x^{m-1}y^{n-1}}{1-x^m y^n}\)
when |x|, |y|<1.
(We write (m,n) to denote the g.c.d of m and n.)
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2010-3 Sum,
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