Re: Fermat extended - Only for mathemathicians
- Posted by "Carl W." <euphoria at cyreksoft.yorks.com> Aug 19, 2002
- 489 views
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