中文摘要：

用模型论的方法证明了一类不定方程a1x^r1^1＋a2x^r2^2＋…＋anx^rn^n=by^s（其中a1,…,an,b为任意整数,r1,…,rn,s为任意正整数）有解.进一步地,我们用相同的方法解决了一个猜想.

英文摘要：

By using model-theoretic methods, it is verified that one type of the diophantine equations a1x^r1^1＋a2x^r2^2＋…＋anx^rn^n=by^s（a1,a2,… ,an, b are integers, r1 ,r2 ,… ,rn, sare positive integers） have solutions. Furthermore, a conjecture is solved by applying the same methods.