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

Versione 1.022/3/2013Pagina 21 di 4924πWe note that in the inequality k < 2 = 2,7938…, we have 24, number that is connected with the24 − πmodes corresponding to the physical vibrations of the bosonic strings by the following Ramanujanfunction:⎡∞ cosπtxw'2−πxw'⎤⎢ ∫ e dx0⎥4⎢antilog coshπx2⎥ ⋅πt− w'⎢4( ) ⎥=⎣e φw'itw'24⎦⎡ ⎛ 10 + 11 2 ⎞ ⎛ 10 + 7log⎢⎜ ⎟ + ⎜⎢⎣ ⎝ 4 ⎠ ⎝ 41422t w'2 ⎞⎤⎟⎥⎠⎥⎦.Furthermore, we note that 1,3333…< k < 2,7938… are very near to the following values: 1,33333333and 2,79256959, (the first is equal) values corresponding to frequencies concerning the musical systembased on the Phi (i.e. the aurea ratio 1,61803398…)k = 21 + b 4 = c 2with two unknowns b and cBut for what value of n we have that k = 2hence we have solutions if and only if1 + b n = c 261 1+⎝ 22π = 0,6079… < ⎛ ⎞⎜ ⎟n ⎠< 1