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

Versione 1.022/3/2013Pagina 23 di 49Since the equation is symmetric1 + b n = c kis equivalent to solve the unknown n or kSo, for example, we LIMIT the field equations valid1 + b 2 3, 4, 5, 6, 7, 8, 9= c1 + b 3, 4, 5, 6, 7, 8, 9 = c 2Solving this set of equations of only 14 equations, we find the only possible solution is thefollowing1 + 2 3 = 3 2Thus, for example, it isn't possible to have an equation as1 + 10 3 = 2,68 7Apart from the fact that c is not an integer, what is important to note is the value of the exponent of2πthe inequality abc that exceeds the maximum value of = 1,64496(rad (10*2,68)) q = 2,68 7q = 2,098 > 1,6449that's no good and it shows that all the other infinite equations with any n and k aren't possible,except field equation above.Notes that the field equations have n exponent or k exponent equal to 2, otherwise we don't havesolutions.This occurs also in the general case of the conjecture of Fermat-Catalan where one of theexponents m or n or k is equal to 2.