Article contents
Pairs of additive congruences: cubic congruences
Published online by Cambridge University Press: 26 February 2010
Abstract
We consider two additive cubic equations
in p-adic fields. Davenport and Lewis showed that the equations have a non-trivial solution in every p-adic field, if n ≥ 16, and need not have a solution in the 7-adic field, if n = 15. Here we prove that if p ≠ 7 the equations have a non-trivial solution in p-adic fields if n ≥ 13. When n = 12 such a result fails for every prime p ≡ 1 (mod 3).
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 1985
References
- 4
- Cited by