AI 中文总结
本文研究算术级数中的Erdős-Moser方程，证明k=2时该级数若有解必含两项或四项，且两种情况均存在无穷多可完全刻画的解。
AI 中文摘要
我们研究算术级数中的Erdős-Moser方程 $1^k+2^k+\cdots+(m-1)^k=m^k$。我们证明，当k=2时，该算术级数中的和若存在解，则必须包含两项或四项；在两种情况下，均存在可完全刻画的无穷多解。
英文摘要
We consider the Erdős-Moser equation $1^k+2^k+\cdots+(m-1)^k=m^k$ in arithmetic progressions. We prove among other things that when $k=2$, for any solution to exist, the above sum in arithmetic progression must consist of two or four terms. In either case, there are infinitely many solutions that can be completely characterized.
Comments14 pages, 3 figures
