abcalphabeta Posted September 16, 2010 Share Posted September 16, 2010 f(f(n-1))=f(n+1)-f(n) if a solution exists (which i somehow doubt but am unable to prove) Link to comment Share on other sites More sharing options...
Bignose Posted September 16, 2010 Share Posted September 16, 2010 At least one solution exists f(n)=0. It is rather trivial, though. Link to comment Share on other sites More sharing options...
the tree Posted September 18, 2010 Share Posted September 18, 2010 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 Link to comment Share on other sites More sharing options...
abcalphabeta Posted September 18, 2010 Author Share Posted September 18, 2010 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. Link to comment Share on other sites More sharing options...
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