Let $s_0,s_1,s_2,\dots$ be a sequence of rational numbers whose mth divided difference ${\delta }_{m}s$ is integer-valued. We prove that $s_n$ is a polynomial function in n if $|s_n|\ll {\theta }^n$ for some positive number θ satisfying $\theta <e^{1+\frac{1}{2}+\cdots +\frac{1}{m}}-1$.

中文翻译：

---

具有整数值除差的函数

让 $s_0,s_1,s_2,\dots$是一个有理数序列，其m次除差${\delta }_{米}s$是整数值。我们证明$s_n$是n中的多项式函数，如果$|s_n|\ll {\theta }^n$对于某个正数θ满足$\theta <e^{1+\frac{1}{2}+\cdots +\frac{1}{米}}-1$.