Sklansky -Fermat Conjectures

[David Sklansky]

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.

[Roland19]

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

[Daliman]

[ 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

[Roland19]

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.

[nate1729]

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

[kurosh]

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

[BarkingMad]

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.

[kurosh]

You misunderstood.

[Sponger15SB]

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

[TimTimSalabim]

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.