【摘要】 <正> §1.設k>1是一個固定的正整數,則每一個正整數x都可以唯一地表成 x=a₁kⁿ1+a₂kⁿ2+…+a₁kⁿt,其中n₁>n₂>…>n_t≥0都是整數;a₁,…,a_t也都是正整數且≤k-1.我們令,並令.在k=2的情况,文[1]的作者們證明了更多还原

【Abstract】 Let k≥1 be a fixed integer, then any positive integer x can be uniquely represented by the following form x = a₁ kⁿ¹ + a₂ kⁿ² + … + a₁ kⁿ¹, where n₁> n₂ > … > n_t ≥ 0 are integers, and a₁, …, a_t are also positive integers not greater than k-1. Define a（x）Theorem 1. For any k≥2, we have Moreover, the result is the best possible.Let m be a fixed integer, then the equation a（y）=m has infinite many solutions. Let B_m（x） be the number of solutions not greater than x, we haveTheorem 2.更多还原