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Suppose A1A_{1}A1A2A_{2}A2A3A_{3}A3…\ldots…AnA_{n}An is an nnn-sided regular polygon such that
1A1A2=1A1A3+1A1A4.\frac{1}{A_{1}A_{2}}=\frac{1}{A_{1}A_{3}}+\frac{1}{A_{1}A_{4}}.A1A21=A1A31+A1A41.
Determine the number of sides of the polygon.
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