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For positive integer n, let Sn denotes t...

For positive integer n, let `S_n` denotes the minimum value of the sum `sum_(k=1)^n sqrt((2k-1)^2 + (a_n)^2)` where ` a_1, a_2 , a_3 ... a_n` are positive real numbers whose sum is 17. If there exist a unique positive integer n for which `S_n` is also an integer, then `(n/2)` is :

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