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abcalphabeta

help on solving a functional equation

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At least one solution exists f(n)=0. It is rather trivial, though.

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A simple proof by contradiction should at least show that there are no non-trivial linear solutions.

 

(*) f(f(n-1))=f(n+1)-f(n)

assume f to be linear

f2(n-1)=f(1)

f(n-1)=1

f=1

(*) 1=1-1 //

so f is not linear

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whoops i forgot to mention the function is from N to N. so the equation is satisfied for n>=2

 

from this i infer f is strict increasing and f(n+1)-f(n)>=n-3 and many more inequalities.

 

but none leads to any sort of contradiction. :(

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