Function in Function in Function in Function in Function

Algebra Level pending

Let \(f: \mathbb{Z}^{+} \times \mathbb{Z} \rightarrow \mathbb{Z}\) such that

  1. \(f(0,y) = -y\)
  2. \(f(x+1,y) = f(x,f(x,f(x,f(x,f(x,-y)))))\)

Find the value of \(f(31415,92653)\)


This problem is adapted from Thailand 8th Mathematics POSN (1st round preceding 2nd round).

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