A simple proof of FLT
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From: smallfrey on 8 Jul 2010 16:11 If you want to make inferences about FLT from studying small n, you'd be better off considering the equation (a^3+b^3)/(a+b)=c^3 (which has solutions) than Pythagorean triples. This is "almost" a solution of Fermat's equation for n=3 (a+b fails to be a cube). Slight reformulations of the classical Furtwangler and Vandiver theorems are applicable in this case. (See Paulo Ribenboim's "13 Lectures on Fermat's Last Theorem" for an overview of what these theorems are.) This equation has many interesting (and non-trivial) properties.
From: smallfrey on 9 Jul 2010 06:10 Working with rational numbers is not the way to tackle FLT either. In 1850, Kummer claimed that Fermat's equation for "regular" prime exponents has only the trivial solution in the cyclotomic field Q(lambda). There was a lapse in the proof that Hilbert fixed in 1897.
From: smallfrey on 10 Jul 2010 16:05 I'm an addlepate; I wrote "lambda" but I meant that squiggly Greek letter.
From: spudnik on 11 Jul 2010 22:23 well, what did he do, when he got to n=67? (sumorial ?-) > Fermat proved all successes of the exponent 2 are non-successes for exp.4.. I would speculate that Fermat squared the square of the Pythagorean sides to get the fourth power he used in his proof, and that he used fractions in his own explorations. The ancients, I have read, used fractions. Number theory also simplifies overwhelming information. thus&so: so, how about for base-3? -- not "sumorial," if that's not a pun. > "Generalization to digits beyond the first". --les ducs d'oil! http://wlym.com
From: spudnik on 12 Jul 2010 14:53
that what I though -- ba-doom! thus&so: yeah, but are the rubber glasses, 3d, or the clocks? > ... so, I said, "Hey, Einstein, space and time are made of rubber! > "Just kidding, dood." > I am, however, not implying that he was a surfer, but > he did know the canonical surfer's value ... of pi. thus&so: it's just his bot, as far as I can tell, without researching it ... googoling would be way too much positive feedback, and that's unpositively moderate anyway, what difference between lightwaves and rocks o'light, vis-a-vu the curvature of space (as was uncovered by You now who & you know whO-oo, in the 18th and BCE centuries (or 2nd and Minus Oneth millenia ?-) also, don't forget the ... well, their are a few of them! > If colleagues know, what good? thus&so: .... time, considered to be perpendicular to all of the three spatial directions; at least, in some abstract sense. anyway, I invented the terminology; so ,there.... um, perpendicular Universes: --BP's cap™ call of brokers the group! association http://tarpley.net |