摘要
In this paper, the additive equations of the type α_1λ_1~k+ … +α_sλ_s^k = 0 are studied, α_i'sbeing integers of an algebraic number field K of degree n. The main result is as follows: Ifs≥(2k)^(n+1) (or s≥cknlogk for 2 + k), the equation is solved nontrivially in any β-adic field,where β is a prime ideal of K.
In this paper, the additive equations of the type α<sub>1</sub>λ<sub>1</sub><sup>k</sup>+ … +α<sub>s</sub>λ<sub>s</sub><sup>k</sup> = 0 are studied, α<sub>i</sub>’sbeing integers of an algebraic number field K of degree n. The main result is as follows: Ifs≥（2k）<sup>n+1</sup> （or s≥cknlogk for 2 + k）, the equation is solved nontrivially in any β-adic field,where β is a prime ideal of K.
