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Simultaneous diagonal p–adic equations

  • I. D. Meir (a1)
  • DOI:
  • Published online: 01 February 2010

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.

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2.M. Aigner . Combinatorial Theory (Springer, 1979).

4.H. Davenport and D. J. Lewis . Simultaneous equations of additive type. Phil. Trans. Roy. Soc. London, 264A (1969), 557595.

6.W. M. Schmidt . Equations over Finite Fields, An Elementary Approach, Lecture Notes in Mathematics, 536 (Springer, 1976).

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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