# 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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