```Date: Mar 7, 2013 11:29 PM
Author: Brian Q. Hutchings
Subject: Re: From Fermat little theorem to Fermat Last Theorem

Munk said that this must have been Fermat's proof, andI can only verify it up to the very last pageof the alleged proof, which may be poorly stateddue to "English as a second language," althoughit is mostly very elementary.Munk was well-qaulified as a student of Prandtl in aerodynamics,as far as mathematical physics goes, at Goettingen U.;he was one of the pioneers at NACA, the predecessor to NASA,albei mainly with planar slices of airfoils.The book is actually quite amuzing, and he statesin the chapters after the main result, that most mathematicianswould think of his "congruence surds" as "p-adic numbers,which they are not." Yes, the p-adics are a big keyto this, as they are in quantum mechanics, but it is reallyjust a matter of "adding-machine mechanics," which a fewof the classical math-folks had actually developed,before anyone else: Pascal, Liebniz and Fermat.Although the congruence surds have the same problemas p-adics, namely that they have no simple, "archimedeanvaluation" or absolute scalar value, that is not importantto this theorem, which merely proves the impossiblityof certain congruences, teh ones that are akinto the Pythagorean theorem, using exponents other than two.Here, I will just supply a note as to the hearsay about Fermat,not having been able to prove this "miraculous" result,as he wrote in the margin of his _Bachet's Diophantus_ bookof old number problems. Well, he made no other known errors,and this includes the sole remaining unsloved problemof Fermat, the characterization of the Fermat numbers(of the form, 2^(2^h) + 1, h = 0, 1 etc. Well,he had merely congectured that they were all prime, andhe later retracted this ideal in a letter to Bernardde Frenicle; so, theresville.Furthermore, this may have been one of his earliest proofsin the theory of numbers -- which science he created,mostly using right trigona -- and this is highlightedby the fact taht he *later* produced the prooffor teh very special case of the exponent, n = 4. Allof the other cases can be made for only prime exponents,since it is easy to prove that composite exponents-- other than 2x2 -- reduce to the case for prime ones.--sincerely, R. Brian Hutchings
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