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#13
06-18-2005, 05:09 PM
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Re: Sklansky -Fermat Conjectures
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A, B and C have to be distinct values. If you make B = C, then they both drop out of the equation and there's no point to it. [/ QUOTE ] OK, Let... A = 8 B = 7 C = 6 N = 5 and Q = 41799 8^5 = 32768 7^5 = 16807 32768 + 16807 = 49575 49575 - 6^5 = 41799 I guess I'm working the problem backward by assigning values to A B C & N then finding for Q. It also has occured to me that (as suggested by DS) maybe there are very few q's, and I'm just finding them easily by going backward. Of course, it is also possible that I'm messed up like a chowder sandwich, and I'm just not smart/educated enough to see what makes this conjecture intriguing, or what it is that should be difficult about it. 
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#14
06-18-2005, 06:11 PM
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Re: Sklansky -Fermat Conjectures
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I'm just not smart/educated enough to see what makes this conjecture intriguing, or what it is that should be difficult about it. [/ QUOTE ] Yeah, could someone at least point us in the right direction?
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#15
06-18-2005, 06:42 PM
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Re: Sklansky -Fermat Conjectures
After doing some googling, i get it now... I think.
The Sklansky - Fermat conjectures look like Fermats Last Theorem with q as an added twist. I read about this here... Pierre de Fermat According to the link, some wicked smart dude named A. Wiles proved Fermat's Last Theorem in 1995. Can the Sklansky - Fermat conjecture be proved as well? I have no idea. I'll leave that to the Good Will Hunting's of the world.
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#16
06-18-2005, 08:54 PM
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Re: Sklansky -Fermat Conjectures
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Yeah, could someone at least point us in the right direction? [/ QUOTE ] Let me describe how I am reading what Sklansky has said, and maybe this clears it up. Fermat's Theorem: X^n + Y^n = Z^n where n > 2 Fermat says there cannot exist integers X, Y, and Z that satisfy this equation. As far as I know, there is no constraint that X, Y, and Z must be distinct. There is a constraint that n must be greater than 2, otherwise the theorem is obviously false... look at pythagorean triples. Sklansky-Fermat Conjecture 1: A^n + B^n = C^n + Q where n > 4 There exist some values of Q where the above equation cannot have integer solutions for A, B, and C. Sklansky-Fermat Conjecture 2: If you find such a Q where no integer solutions for A, B, and C exist, then it is possible that there is no way to formally prove it. Hopefully this clears up what Sklansky is trying to say. And, Mr. Sklansky, if I misunderstood, please correct my understanding of your problem. -RMJ
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#17
06-19-2005, 12:09 AM
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Re: Sklansky -Fermat Conjectures
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Conjecture One: A to the nth plus B to the nth (when n is an integer, five or greater) cannot equal equal C to the nth plus q, for some if not most q's. Conjecture Two: If there are in fact q's for which the conjecture holds, some will be formally unprovable. In other words it might be true that (A to the n) + (B to the n) can never equal (C to the n) plus (lets just say) the number 846879032 (n greater than four), yet no proof of this fact is even theoretically findable. [/ QUOTE ] Poker must bore the piss out of you.
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#20
06-19-2005, 12:53 AM
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Re: Sklansky -Fermat Conjectures
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Conjecture One: A to the nth plus B to the nth (when n is an integer, five or greater) cannot equal equal C to the nth plus q, for some if not most q's. Conjecture Two: If there are in fact q's for which the conjecture holds, some will be formally unprovable. In other words it might be true that (A to the n) + (B to the n) can never equal (C to the n) plus (lets just say) the number 846879032 (n greater than four), yet no proof of this fact is even theoretically findable. [/ QUOTE ] my head just asplode
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