关于方程≡0（modl）的解个数

ON THE NUMBER OF SOLUTIONS OF THE EQUATION

设ｄ＿１……，ｄ＿ｎ是ｎ个正整数．熟知，不定方程，１≤ｘ＿ｉ≤ｄ＿ｉ－（ｉ＝１，…，ｎ）的解的个数在有限域Ｆ＿ｑ上对角方程的研究中起重要作用．作者分别给出了此方程恰有２组解和恰有３组解的充分必要条件．

Let I(d_1,…,d_n) denote the number of solutions to equation It is investigated that。numbers I(d_1,…,d_n),which play an important role in studying diagonal equations over a finite field. The author obtains a necessary and suffucient condition forI(d_1,…,d_n)=2and(d_1,…,d_n)=3in terms of where