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Related: About this forumLongest maths proof would take 10 billion years to read
From phys.org:
"Boolean Pythagorean Triples" is not a shameful contagious disease, but a long-unsolved enigma within a field called Ramsey Theory.
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It asks if it is possible to colour positive whole numbers (such as 1, 2 or 3) either red or blue such that no sequence of numbers that satisfy Pythagoras's famous equationa2 + b2 = c2are the same colour.
If a and b are red, for example, then c could be blue. But all three could not be blue or red.
greiner3
(5,214 posts)bvf
(6,604 posts)re the abc conjecture.
Lionel Mandrake
(4,077 posts)Just as a search for odd perfect numbers may show that there are none less than some enormous number, such a result does prove that there are none at all.
struggle4progress
(118,379 posts)My current understanding is that it exhibits a specific integer n > 0 such that every 2-coloring of the integers 0<= j <= n contains a monochromatic Pythagorean triple
If this is true, then any 2-coloring of the positive integers would induce a 2-coloring of the integers 0 <= j <= n and so would contain a monochromatic Pythagorean triple
The first part of their accomplishment is finding such a specific integer n > 0
Their n, however, is large enough that a brute computer search through all 2-colorings of the integers 0<= j <= n is infeasible
The second part of their accomplishment is an analysis that reduces the needed computer search to something feasible
The third part of their accomplishment is a program that performs the necessary reduced computer search
But it's still a monster computation by human standards: no human can directly verify the results of the reduced computer search
Jim__
(14,096 posts)This is a link to the paper that describes the proof.
The abstract from the paper: