AI 中文总结
研究具有乘法封闭且和集不与自身相交性质的递增整数序列，判断其是否为极大序列，确定了三个族中序列是否为极大的。
AI 中文摘要
我们研究具有如下性质的递增整数序列：序列中任意两项的乘积仍是该序列中的一项，且任意两项的和不是该序列中的一项。若一个具有上述性质的序列不是另一个具有相同性质序列的真子序列，则称其为极大的。我们确定了三个族中的序列是否为极大的。
英文摘要
We investigate increasing sequences of integers with the property that the product of every two terms of the sequence is also a term of the sequence and the sum of every two terms is not a term of the sequence. We say that a sequence with the above properties is maximal if it is not a proper subsequence of another sequence with the above properties. We determine whether the sequences in three families are maximal or not.
