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\[S=\dfrac{5}{1 \times 3 \times 7}+\dfrac{7}{3 \times 5 \times 9}+\dfrac{9}{5 \times 7 \times 11}+\cdots \]

If \(45S = n^2+ 1\), where \(n\) is a positive integer, find \(n\).

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