AI 中文总结
该研究解决了Hickerson与Kleber提出的问题，给出将任意36个连续整数通过平方差化为零的明确方法，结合已有结果得出整数集可对所有整数n化为零的长度条件为12整除且不小于24。
AI 中文摘要
对于整数的有限多重集，可反复选取两个元素a、b，将其替换为|a²−b²|。Hickerson和Kleber提出问题：对每个整数n，集合{n,n+1,…,n+35}能否化为零？我们给出了明确的化简方法。结合他们对长度12和24的结果，可得对每个正整数L，{n,n+1,…,n+L−1}对所有整数n均可化为零当且仅当12整除L且L≥24。
英文摘要
For a finite multiset of integers, repeatedly choose two entries $a,b$ and replace them with $|a^{2}-b^{2}|$. Hickerson and Kleber asked whether, for every integer $n$, the set ${n,n+1,\ldots,n+35}$ can be reduced to zero. We give an explicit reduction. Together with their results for lengths 12 and 24, this gives, for every positive integer $L$, [ {n,n+1,\ldots,n+L-1}\text{ reduces to zero for every }n\in\mathbb Z \Longleftrightarrow 12\mid L\text{ and }L\ge 24. ]
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