(3) is Leibniz, not Newton.
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I have a proof but it's too small to fit in this tweet.
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One correction, and one remark:* -The correction: the conjecture, by Andrew Beal, dates from 1993 (and not from 1997). -The remark: the A, B, C, x, y and z in the conjecture are all supposed to be positive «integers», and x, y, and z greater than 2. ___ *https://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules …
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was just about to type 3,4,5 right triangle

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The duel is not mysterious: you can read about it in the book “Whom the Gods love: The Story of Evariste Galois”, written by Leopold Infeld. Galois’ theory and life are there. Wonderful book!
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*for x, y, z > 2
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Ah! I was going to say! That's an important omission right there!
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