proof of fermat-catalan conjecture through the ... - Nardelli - Xoom.it

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Versione 1.022/3/2013Pagina 26 di 492 2 2π π π1 6 1−16(1 6) = c 0 = 1instead if e=1 we have:61⎝ m1n2k2π = 0,6079… < ⎛ ⎞⎜ + + ⎟ ⎠< 1a special case with2 2 2π π πB 6 C−16(A 62π) = c 6Of course it must always apply the inequality1 1 1+ + < 1m n kso e is limited by n and kThis shows by the new abc conjecture that we have only finitely many solutions (a,b,c,m,n,k) where(m or n or k) = 2, one of the three, otherwise the inequality doesn't hold.--------------------------------------------------------------------------------------------------------------------------Famous example of RamanujanIn fact there are 2 solutionsa 3 + b 3 = 1729rad (a 3 * b 3 * 1729) > 172912 3 + 1 3 = 1729
Versione 1.022/3/2013Pagina 27 di 49rad (12 3 *1 3 * 1729) = 2*3*7*13*19 = 10374 > 1729or even better (for the quantity or “quality” of the radical)10 3 + 9 3 = 1729rad (10 3 * 9 3 * 1729) = 2*3*5*7*13*19 = 51870 > 1729
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proof of fermat-catalan conjecture through the ... - Nardelli - Xoom.it

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