Re: Rotationally Prime Numbers Revisited

I was going to say that proving a "negative statement", is logically impossible...

However, this is mathematics, so perhaps the "I can't prove I don't have something, you have to prove I do" isn't quite as solid in the world of mathematics? I'm pretty sure reading through some of the recent mathematical threads I've seen some "proofs" that showed that certain things are not possible.

But, I could simply be remembering "conjectures" and the like as "proofs", and thus, the original line above might still be correct?

-Scott

Comment on Re: Rotationally Prime Numbers Revisited

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Re^2: Rotationally Prime Numbers Revisited by shemp (Deacon) on Mar 25, 2005 at 00:58 UTC
It is perfectly valid in math to prove that something does not exist. For example, there are no positive integers {a,b,c} such that a^3 + b^3 = c^3 This is a direct result of Wiles (1994) proof of Fermats Last Theorem. Now there are also a different class of assertions that cannot be proved either way. (Godels Incompleteness Theorem) I am digressing a lot here, but if you find this sort of thing interesting, i suggest reading 'Godel, Escher, Bach' by Hofsteadter (spelling?) ...prepare to hurt your brain :)	[reply]
Re^3: Rotationally Prime Numbers Revisited by ambrus (Abbot) on Mar 25, 2005 at 09:27 UTC
For example, there are no positive integers {a,b,c} such that a^3 + b^3 = c^3 This is a direct result of Wiles (1994) proof of Fermats Last Theorem. No, this case is much easier to prove than the general case, and was proven in the 18th century by Euler and Legendre. In fact, for all sufficently small n exponents the impossibility of a^n + b^n = c^n was proven long ago, in fact, Szalay[1] which was published in 1991 reports all n < 125000. [1] Dr. Szalay Mihály, Számelmélet. Tankönyvkiadó, Budapest, 1991	[reply]
Re^4: Rotationally Prime Numbers Revisited by tilly (Archbishop) on Mar 25, 2005 at 19:36 UTC
The fact that there is an easier proof of the special case doesn't change the fact that the special case is a direct result of the general case.	[reply]