Re: Fermat extended - Only for mathemathicians
rforno wrote:
> Carl W. wrote:
>
> [IIRC there's] a counterexample matching x^4 + y^4 + w^4 = z^4 ...
>
> > With your data, I wrote a small program in C (for speed) trying to
> > find the counterexample with 3 elements and exponent 4. It failed
> > to encounter any case up to 194 as the maximum value of each element
> > (I imposed this limitation in order to have the numbers in the
> > unsigned long range). I will try it again with higher values using
> > long double numbers, but I don't think I will get some answer. Maybe
> > the only way to find a counterexample will be to use big numbers
> > arithmetic, such as the one available in the ABC language, but it will
> > take a looooong time.
I owe you an apology since I omitted a critical piece of info in my last
post. While I didn't remember the numbers involved for x, y, w and z, I
*did* know that they were quite large - being eight or nine digits apiece. I
should have at least said that... Sorry. :(
Searching for equations in Google is a pain, which is why I didn't do that
before. This time I persevered and turned this up:
http://www.discover.com/may_02/bogglers.html
...and somewhere near the bottom is this beauty:
2682440^4 + 15365639^4 + 18796760^4 = 20615673^4
In case you're wondering this is the *smallest* power 4 counterexample. :)
HTH,
Carl
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