11S Three ways to attack a functional equation

11. PEN K11 (Canada 2002) Find all functions such that for all
:

Here, denote the set of all nonnegative integers.
Here is the official solution file: pen11.pdf.
You can also discuss the problems here!

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11. Three ways to attack a functional equation

Hi everyone. PEN is BACK. Here goes the first problem of the second season!
11. PEN K11 (Canada 2002) Find all functions such that for all
:

Here, denote the set of all nonnegative integers.
This problem is suggested by Alexander Remorov from Canada. Next week, his solution will be posted!

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