Mathematika

Research Article

Simultaneous diagonal p–adic equations

I. D. Meira1

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.

Abstract

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)

Key Words:

  • 11D79: NUMBER THEORY: Diophantine equations; Congruences in many variables.