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Fermat-like tuples

by John D'Errico

26 Feb 2006 (Updated 03 May 2006)

Code covered by BSD License

Searches for Fermat-like tuples: x1^n + x2^n + ... + xp^n = z^m

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Description

I thought it might be fun to provide a tool to find Fermat-like tuples. These are sets of p+1 positive integers for which

x1^n + x2^n + ... + xp^n = z^m

Yes, when p == 2 and n == m >= 3, whats-his-name has assured us that we won't find any solutions. But what happens for different values of n and m? Are there solutions when n=2 and m=3? What properties do those solutions have?

Have fun with it. I've also cited a few other tools on the file exchange for those who wish to play with some simple number theory in Matlab. Look around though. I know of at least a few others.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Fermat Last Theorem, Lucas.m, EPRIMES, Collatz

MATLAB release

MATLAB 7.0.1 (R14SP1)

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Everyone's Tags	fermats last theorem pythagorean triples tuples
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Updates
28 Feb 2006	Cleaned up the documentation, added some followups and a warning to signal when numerical problems are likely.
03 May 2006	Extension to p-tuples of numbers

Tag Activity for this File
Tag	Applied By	Date/Time
fermats last theorem pythagorean triples tuples	John D'Errico	22 Oct 2008 08:16:50

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