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I have been told that resources like Mathematica's Number Recognition (which I've never tried myself) and the Inverse Symbolic Calculator (ISC) can be used to find possible closed forms for real numbers (with many known decimal digits).

But I would like to know if there are similar resources (preferably free ones) that work for rational numbers or integers (even large integers). In particular, I'm searching for some program which can:

  • find "complex" ways to express a number (for example, by using particular constants or functions);
  • find expressions of a number in terms of sums of squares, squares roots, cube, cube roots, sum of prime numbers, and other things.

Note: I know that Wolfram Alpha can do such things, but the limited computation time doesn't allow to have many results.

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    $\begingroup$ Maple has a good identify command and a PSLQ both can express a constant in terms of known constants. Sage also has this feature. Mathematica has it to a lesser extent but it is not too difficult to write a routine that can do what you require. $\endgroup$ Commented Oct 4, 2014 at 9:29
  • $\begingroup$ If you own a copy of Maple, can you tell me some examples of output. For example, what is the output given 133245? $\endgroup$ Commented Oct 10, 2014 at 21:23

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For example, what is the output given 133245?

$ 168^2+179^2+188^2+194^2=133245 $

$ 6^3+13^3+18^3+50^3=133245 $

Those are just two examples of what can be done but I used Mathematica instead.

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  • $\begingroup$ Really good. Thank you. $\endgroup$ Commented Oct 11, 2014 at 14:37
  • $\begingroup$ You are welcome. $\endgroup$ Commented Oct 12, 2014 at 1:51
  • $\begingroup$ Can you tell me what code you used in Mathematica? $\endgroup$ Commented Oct 14, 2014 at 15:39
  • $\begingroup$ PowersRepresentations[133245, 4, 2] PowersRepresentations[133245, 4, 3] you will get lots of answers, choose the one you like. $\endgroup$ Commented Oct 15, 2014 at 4:33

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