[psyang]

Originally Posted by Mathgod

Spoiler!

Click for solution attempt:

Spoiler!

Tried replacing f(x) with x in the final 2 lines. The first one evaluates to n=1. The 2nd one appears to be generally true.

So my guess for the solution is n=1 and n ≡ 3 mod 4

I like the idea, but

Spoiler!

n=5 and n=11 would be simple counter examples (one works when it shouldn't, the other doesn't work when it should).