a1 Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH. Tricorder Technology plc, The Long Room, Coppermill Lock, Summerhouse Lane, Harefield, Middlesex UB9 6JA.
It is known that a system of r additive equations of degree k with greater than 2rk variables has a non-trivial p-adic solution for all p > k2r + 2. In this paper we consider the same system with more than crk variables, c > 2, and show the existence of a non-trivial solution for all p > r2k2+(2/(c − 2)) if r ≠ 1 and p > k2+(2/(c − 1)) if r = 1.
(Received January 25 1996)