# find a function given some values

I'me trying to remember my math classes but no luck... I've got a pair of values i.e .

1085520->221
17447319->1202
347863118->3484
1561584711->59427
1734973510->73582
1578039135->70836


Is there a way that I can find the function associated to that so I can calculate it for any X.

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Try to search Lagrange interpolating polynomial. – Giuseppe Nov 15 '11 at 13:35
In fact, there are infinitely many functions which have those values! – Tigran Hakobyan Nov 15 '11 at 14:16

You are asking for "the" function, but as Tigran notes in the comments there are many many many functions that will give you those 6 values (and then differ from each other when you put in a different $x$). The only way to make progress is to know something about the type of function you are looking for. So let's go back to the beginning.
If it's the latter, you are out of luck. Tigran's comment applies, and the value corresponding to, say, $x=10,000,000$, could just as easily be 1,000 as $\pi$ or $-\sqrt2$ or $49867584932/409685753421$ or anything else you care to name.