Sklansky -Fermat Conjectures
 

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.

Re: Sklansky -Fermat Conjectures
 

David Sklansky, you just made my night. You're my hero.

Re: Sklansky -Fermat Conjectures
 

[ QUOTE ]
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 ]

DUUHH

Re: Sklansky -Fermat Conjectures
 

Honestly, though, I'd be interested to hear the relevance this has to anything. Where did this come from and what does it mean? I'm no math wizard, but sometimes I like to pretend that I am, and if I knew what the hell you were talking about, that would help further my pursuit of witchcraft and wizardry. Harry Potter out.

Re: Sklansky -Fermat Conjectures
 

David --

What motivates these conjectures? They "ring true" to me in the sense that they strike my mathematician's instinct as meaningful and not extremely likely (were I to lay odds) to be false; I do not, however, know enough of the technical material at the bottom of Wiles' proof to know if these conjectures would arise naturally from a careful consideration of it. (The reason I ask is that they also seem like they might have arisen from just idle thinking about Fermat's conjecture.)

And if you're trying to prove these and there's a lemma or two a guy with a BA in math from a good university (I studied mostly algebra and analysis) might be able to sink his teeth into, please PM me.

--Nate

Re: Sklansky -Fermat Conjectures
 

Ok? What's your point? Do you want someone to try and prove/disprove it?

Re: Sklansky -Fermat Conjectures
 

I'm no mathmetician. So, maybe some of the criteria flew over my head, but I plugged the formula into Excel, inserted some simple numbers for the A-B-C values, and used solver to find "Q".

For N = 5
A = 5
B = 4
C = 4
Q = 3125

5^5 + 4^5 = 4149

4^5 + 3125 = 4149

Again, maybe some of the constraints of the "conjecture" flew over my head. If I understood it correctly though, it seems like there are many Q's for which the conjecture would hold true.

Re: Sklansky -Fermat Conjectures
 

You misunderstood.

Re: Sklansky -Fermat Conjectures
 

[censored] I was totally gonna make this exact post and you beat me to it!

Re: Sklansky -Fermat Conjectures
 

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.