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Let $\Bbb{Z}^+$be the set of all non-negative integers where $n$ and $k$ are given natural numbers. We consider the following non-decreasing function,

$$f:\Bbb{Z}^+ \to \Bbb{Z}^+$$ such that

\begin{align} f\left(\sum_{i=1}^{n} a_{i}^{n}\right) =\frac{1}{k}\sum_{i=1}^{n} \left(f(a_{i})\right)^{n}\\ \end{align}

1.Find all functions for $n=2014$ and $k=2014^{2013}$

2.Find, number of functions which satisfy the condition of the problem depending on the values ​​of parameters $n$ and $k$.


marked as duplicate by Travis, Hamou, Macavity, Martin Sleziak, drhab Oct 14 '14 at 11:37

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ @Travis, this question is not answered there (answer is not full) $\endgroup$ – santoni7 Oct 14 '14 at 10:24
  • $\begingroup$ @santoni7 Then you could ask there for someone to complete it, not sure why you think starting a duplicate will solve the problem. $\endgroup$ – Macavity Oct 14 '14 at 10:43
  • $\begingroup$ I know, but the question is still a duplicate, and having two threads for the same question will make it harder, not easier, to access discussion of it. $\endgroup$ – Travis Oct 14 '14 at 11:15