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Let bj and m be certain integers. In this paper we obtain a bound for prime solutions pt of the diagonal equations of order k, bxp\ + • ■ ■ +/>,./>* = m. The bound obtained is C<logS|2 + C\m\i/k where B = max, {e, \bj\) and C are positive constants depending at most on k.

Bounds of prime solutions of some diagonal equations.