[Fractint] Extended Fermat's Last Theorem - Slightly Off-topic

Does someone in the list know if the following conjecture, that includes as a particular case Fermat's Last Theorem, has ever been posed, and proved false or true? x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no integer solutions. TIA.