My 16th Birthday Problem

Geometry Level 3

If \(f(x) = \sec(\arctan(x))\), find the value of \(f(f(f(f(...(f(1))))))\), where the function is iterated 2015 times.

If you get your answer as \( a \sqrt b\), where \(a\) and \(b\) are positive integers with \(b\) square-free, submit \(a+b\).

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