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| - After more than three hundred years, the mystery of the infamous Last Theorem postulated by Fermat was conclusively disproved by an unlikely bunch of unrelated silly people. The Last Theorem was postulated by Pierre de Fermat, a famous lawyer and mathematician. Fermat's Last Theorem states that: or, even more obscurely: Other than its proven connection with the Apocalypse and the end of the universe, the Last Theorem is of little or, more precisely, no consequence.
- Following his death, a mathematical formula was found scrawled in the margin of his notes, "xn + yn = zn, where n is greater than 2," which Fermat said had no solution in whole numbers, but he also added a phrase, "remarkable proof." Jadzia Dax stated that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." (DS9: "Facets")
- FLT 8-19-11 6-25a There may be a key to Pierre Fermat's conceptualization. Fermat did not assert that there is no A or B such that there can be a solution. He asserted there is no cube added to another cube such that there can be a solution. ( p265, Devlin, K., Mathematics the New Golden Age, 1999, p265 .) Fermat's point of departure was A^ N^ and B^ N^. To work from Fermat's perspective one has to let go of the question, is A or B irrational.
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| - Following his death, a mathematical formula was found scrawled in the margin of his notes, "xn + yn = zn, where n is greater than 2," which Fermat said had no solution in whole numbers, but he also added a phrase, "remarkable proof." According to Jean-Luc Picard, people had been trying to find the proof for 800 years, including himself, during his leisure time. Picard found it stimulating, and noted that it put things in perspective stating that "in our arrogance, we feel we are so advanced and yet we cannot unravel a simple knot tied by a part-time French mathematician working alone without a computer." (TNG: "The Royale" ) Jadzia Dax stated that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." (DS9: "Facets") "The Royale" aired in 1989 , six years before a proof for Fermat's last theorem was published by Andrew Wiles of Princeton University, using advanced 20th century mathematics. Fermat's original proof is still unknown, with many mathematicians suspecting that Fermat was mistaken in believing he had solved the problem. Although on face value it might seem that The Royale introduced a continuity error by not knowing the problem would be solved by the 24th century, Picard's statements is consistent with him being interested in trying to find the original proof. [1] In the script of "Facets" , Tobin starts trying to explain to Jadzia that "The thing you've got to remember when you're trying to normalize the equations is...", before interrupting himself. This dialogue was cut.
- After more than three hundred years, the mystery of the infamous Last Theorem postulated by Fermat was conclusively disproved by an unlikely bunch of unrelated silly people. The Last Theorem was postulated by Pierre de Fermat, a famous lawyer and mathematician. Fermat's Last Theorem states that: or, even more obscurely: Other than its proven connection with the Apocalypse and the end of the universe, the Last Theorem is of little or, more precisely, no consequence.
- FLT 8-19-11 6-25a There may be a key to Pierre Fermat's conceptualization. Fermat did not assert that there is no A or B such that there can be a solution. He asserted there is no cube added to another cube such that there can be a solution. ( p265, Devlin, K., Mathematics the New Golden Age, 1999, p265 .) Fermat's point of departure was A^ N^ and B^ N^. To work from Fermat's perspective one has to let go of the question, is A or B irrational. The construction here begins by defining A as always rational. The expansion of any rational A always produces a rational A ^N^. Pierre Fermat worked with rational numbers, I.e. , with A^N^+ B^N^ = 1, rather than A^N^+B^N^ = C^N^ (Devlin, ibid, p282.) Since B ^N^ =(1- A^N^), then, by substitution A^N^+ B ^N^= 'A^N^+ (1-A ^N^' )= 1. By constructing this problem with A always rational, which always produces a rational A^N^ , then (1- A^N^) is also always rational. For any rational A and for any N>2, these three knowns are always present, are always rational, and would always follow the same principles. Since the A's are the only possible rational numbers, the expansion to any A^N^'s yields the only possible rational quantity. For (1-A^N^) to be a part of a solution it has to have the same quantity as one of the A^N^ 's. The Fermat question can be expressed most simply as, for any N>2, can a (1-A^N^) have the same quantity as a A^N^? This construction completely avoids the nature of B. There is no need to prove that B is always irrational. One proof Fermat had written was 2 ^N^-2 gives a number that can be divided by that N , also written 2 ^N^-2 modN (Stark, H.M., An Introduction To Number Theory, 1994, MIT Press.) 2^ N^-2 is also A ^N^-2 when A = 2 of A ^N^+ (1-A ^N^) = 1, The way the equation is constructed makes a difference in exploring the issues of the problem. For instance, using the A ^N^+ (1-A ^N^) = 1, organizes and simplifies the information such that it is easier to observe essentials, possibilities and alternatives. Constructing an approach that begins with a rational A, a rational A ^N^, and a rational (1- A ^N^), then for any N>2 these three knowns are always present, are always rational, and would always follow the same principles. For all rational sequences of A (0,1), i.e.,{.1,.9}, ... {.000...1,.999...9}, every sequence begins with a “1” as .1, .01, .001, .0001, ... .000...1, and this “1” to any power of N creates an A ^N^ with a “1” as the only digit. No matter what the A^N^ is, the “1” is the begining of the sequence. The next in the sequence is a “2”, as .2, .02, .002, .0002, ... .000...2, and this “2” to any power of N creates an A ^N^ with Fermat's 2 N. P.K Tam, in the Southeast Asian Bul of Mathematics v32 , 2008, p1177-81, presents proofs that Fermat's Last Theorem can be understood in “a self-contained elementary and purely algebraic treatment” (p1177). This article has not been discussed in the West. His paper supports the present thesis, which is a “self-contained elementary and purely algebraic treatment.” Another paper ignored is E. E. Escultura's “An Exact Solution of Fermat's Equation ” Non-Linear Studies v5, 1998, p227-255, in which he demonstrates that “the loss of certainty affects all concepts and propositions involving... infinite spaces.” The present approach constructs this problem with A always rational, which always produces a rational A^N^ , then (1- A^N^) is also always rational. For any rational A and for any N>2, these three knowns are always present, are always rational, and would always follow the same principles--and never involves “infinite spaces.” This paper is on the side of Tam, presenting a simple construction that avoids the pitfalls of infinite spaces and has no constraints due to “loss of certainty.” Escultura's telling criticism contributes to a construction avoiding “pitfalls of infinite spaces.”
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