J Austral Math Soc Ser A 55 pp355--368, 1993.

Three Additive Congruences to a Large Prime Modulus

O. D. Atkinson, J. Brudern and R. J. Cook

(Received 15 January 1991)

Abstract

Let k ł 3 and n > 6k be positive integers. The equations

f(x) = a₁x₁^k + ... + a_nx_n^k = 0,

g(x) = b₁x₁^k + ... + b_nx_n^k = 0,

h(x) = c₁x₁^k + ... + c_nx_n^k = 0,

with integer coefficients, have nontrivial p-adic solutions for all p > Ck⁸, where C is some positive constant. Further, for values k ł K we can take C = 1 + O(K^-˝).

1991 AMS Subject Classification: 11D68

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Authors

O. D. Atkinson
J. Brudern
R. J. Cook

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Last Modified: Fri Jan 10 8:53:39 2003