
#19
Aug3007, 11:08 AM

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#20
Aug3007, 01:11 PM

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One way to go about solving it would be that a power of 4 for example can be expressed in terms of 2*2 or algebraically, 'p=mn' (a^m)^n + (b^m)^n = (c^n)^n Perhaps we could somehow use this identity(though I don't know how). 



#21
Aug3007, 01:39 PM

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Yes, as i said you don't have to check all infinite 'n' just the infinite number of prime 'n'.
Since any nonprime 'n' can be expressed as the sum of 2 prime, another tricky one to prove by the way! 



#22
Aug3007, 04:21 PM

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yes it is, since you had no explanation of why it did not terminate, that is complete BS. Example? OK, find an integer solution of 42323245673565835789467946805234545765831346256725764x^6+ 1356468356835783234623456724689514123412354513487654794679745x^5+264653 24643257654876925634145232534165436457546879856986986735784698659623453 4x^2+x+1 or show none exists. Please, start your computer program now..... 



#23
Aug3007, 08:02 PM

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On the other hand, if you can prove that your program will not terminate, then you can conclude that there are no solutions. 



#24
Aug3007, 10:21 PM

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#25
Aug3107, 12:08 AM

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http://primes.utm.edu/glossary/page.php?sort=LawOfSmall
contains a couple of examples of the misleading behaviour of small numbers. I particularly like Skew's number. I remember another one about sums of powers as well, (perhaps the sum of 4 4th powers) that has only exceptionally large counter examples. 



#26
Aug3107, 02:39 AM

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There was something called the Euler Conjeture: It takes n nth powers to make an nth power. This was largely accepted until it was shownby virtue of a zero for the fifth left term, I have been told, that 27^5 + 84^5 +110^5 + 133^5 = 144^5. A larger case discovered in 1967 as well is: 85282^5 + 28969^5 +3183^5 + 55^5 = 85359^5. (It is interesting to note that 85359^5 = 4.53..x10^24, large enough to suite me.)
Also I am sure people know just as 3^2+4^2= 5^2, we have 3^3+4^3+5^3 = 6^3. Well it is sort of interesting that 4^5 + 5^5 +6^5 +7^5 +11^5 = 12^5. 



#27
Aug3107, 06:25 AM

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#28
Aug3107, 06:37 AM

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#29
Aug3107, 06:53 AM

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From post 1 by ron_jay:




#30
Aug3107, 07:03 AM

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Let's say I name it the "NONTerminating Program Conjecture". 



#31
Aug3107, 07:14 AM

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#33
Aug3107, 10:52 AM

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ron_jay was just saying that he conjectured... he made a guess... Then he looked up Fermat's last theorem and his guess turned out right. It was just supposed to be about how he came across FLT... not that he had justified it or validated it.
Whether or not the guess is unjustified, the fact is that the guess turned out to be true... Do all guesses need to have some sort of proper justification? It's just a guess after all... 



#34
Sep107, 03:04 AM

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Sometimes too much mathematical rigor destroys mathematical intuition, which in my opinion is more important. As robert_ihnot pointed out, even Euler has been guilty of the mistake: Not seeing any counter examples, so believes in the theorem for all examples. It is true, these days with the ever more complex maths, large counter examples are becoming more common, and matt grime, being a modern day mathematician, has good reason to be careful of them. He is merely trying to teach others to be the same. 



#35
Sep107, 05:49 AM

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Ok, root, then.



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