Let a, b, c, d be positive integers. If \frac{1}{a+\frac{1}{b+\frac{1}{c+\frac{1}{d}}}}=\frac{17}{60} then what is the product of a, b, c, d?

Explanation

Inverting the fraction gives \frac{60}{17} = 3 + \frac{9}{17} \implies a=3. Continuing: \frac{17}{9} = 1 + \frac{8}{9} \implies b=1. Next, \frac{9}{8} = 1 + \frac{1}{8} \implies c=1, d=8. Product = 3 \times 1 \times 1 \times 8 = 24.

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