Forwarded message:
From: "Blake Buzzini" <bab282@psu.edu> Subject: RE: Goldbach's Conjecture (fwd) Date: Thu, 19 Nov 1998 23:37:09 -0500
From _Elementary Theory of Numbers_ by William J. LeVeque, pg. 6:
"It was conjectured by Charles Goldbach in 1742 that every even integer larger than 4 is the sum of two odd primes. (All primes except 2 are odd, of course, since evenness means divisibility by two.)"
Ok, so this one says it was Goldbach himself and in particular states two odd primes completely eliminating 4 from the get go ...
From _Excursions in Number Theory_ by C. Stanley Ogilvy and John T. Anderson, pg. 82:
"Goldbach's conjecture. Is every even number expressible as the sum of two primes?"
This one is the second version...
From _Goldbach's Conjecture_ by Eric W. Weisstein (http://www.astro.virginia.edu/~eww6n/math/GoldbachConjecture.html):
"Goldbach's original conjecture, written in a 1742 letter to Euler, states that every Integer >5 is the Sum of three Primes. As re-expressed by Euler, an equivalent of this Conjecture (called the ``strong'' Goldbach conjecture) asserts that all Positive Even Integers >= 4 can be expressed as the Sum of two Primes."
And finaly a third completely different slant. They at least get Fermats contribution right.
Am I misreading somewhere?
Well I'd say that all three of your references tended to contradict each other. Which one do you want to stand on? This is my quote:
No, that was Fermat, Goldbach just says every even number greater than two can be represented as a sum of primes. Basicaly Fermat says that if we have n primes we can reduce them to 2 primes only, in all cases. Which happens to exclude using equilateral triangles as a test bed since you can't tile a equilateral with only two other equilaterals, you could use rectangles though. So basicaly from a geometric perspective Fermat says that given a rectangle of even area it is possible to divide it with a bisector into two rectangles of prime area.
It's interesting that Fermat doesn't mention that the only prime that can use two as a factor is 4. And you can't factor 2 at all since we eliminate 1 as a potential candidate (another issue of symmetry breaking simply so we don't have to write '....works for every prime but 1' on all our theorems).
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