I want to approximate a very large number in a small way. I have looked at geometric progression (which I can just about understand), but it seems to only work forwards. I want to supply a very large number and come up with a formula that will represent an approxmation of that number. The formula needs to be compact and very small. Somthing like... 2342342134213423423423423213424..... (thosands of digits) = 123^45 - 12^12 The object it to have the formula part (i.e. 123^45 - 12^12 ) very small. I realise that the formula will be an approximation and will be need to have a remainder that is still a very large number. I could then calculate the formula again on the remainder, and so on until I end up with a whole series of formulas and a manageable sized remainder. Can anyone help me with what I want to do?