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My Faux Pas Proof of Fermat's Last Theorem DOES PROVE that no diophantine equation exists (in integers) for x^n + x^n = z^n for n > 2. But...in case you haven't figured it out yet, my Faux Pas Proof of FLT fails because I assigned a single variable, d, to increase the 1st segment of z^n by the exact decrease in the remaining segment of z^n where z^n may be viewed as a diameter with two radii of x^n each. Now x, n and z are fixed constants. But that "single" variable, d, does double duty which is impossible. That single variable, d, gets modified by n, which changes its relationship to the other variables. Look for my differential proof of FLT which assigns relationships between variables at the infinitesimal level. For example, if one d, say d_1 changes at one rate, the other d, d_2 changes at another rate. We can compute any unknown variable given the others using calculus. Would you like to read more about Fermat?
Send me some details and I'll see what I can do. Look for Simon Singh's "Fermat's Enigma, The Epic Quest to Solve The World's Greatest Mathematical Problem." Here's a direct link to that popular novice level book to save you some time:
If you want a more in depth introduction to number theory, you might enjoy George E. Andrews paperback, "Number Theory." Click below for a direct link: Of course, a timeless classic that introduces you to the life and times of Fermat among others is Eric Temple Bell's "Men of Mathematics." (By the way, there is some mention of Sophie Germain in the section about Gauss.) Click HERE for Men of Mathematics by E. T. Bell -- You just have to have this one. Other books I enjoyed (and will discuss) include these: Click HERE for QED: The Strange Theory of Light and Matter by Richard Phillips Feynman -- written in non-technical terms for just about everyone. Do not miss this, whatever you do! |
