I did more than that. The method of least squares yielded a "nice looking polynomial". In reality you are true about being able to find any polynomial for any sequence they are just sometimes "ugly looking" and I assume that is not want Ranger really wants.

------------

I devolped a theory sometime ago about being able to find

a polynomial that fits the sequence exactly.

I was able to demonstrate (incompletely) that given a sequence

then you can find a

**Unique** polynomial of degree

which maps

.

I never got to fully completing this theory. Some results were very difficult to prove. Perhaps you can help me complete it if I post it on this forum. One day people will refer to it as the Black-Hacker Theory (dreaming).