A series of 3 numbers B(1),B(2) and B(3) are defined to be in Arithmetic Progression if B(3) - B(2) = B(2) - B(1).

Without referring to Fermat's Last Theorem, prove that it is not feasible to determine three positive integers in Arithmetic Progression with the nineteenth power of the largest integer being equal to the sum of nineteenth powers of the remaining integers.