1 results
A NOTE ON THE SUM OF RECIPROCALS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 2 / October 2019
- Published online by Cambridge University Press:
- 17 May 2019, pp. 189-193
- Print publication:
- October 2019
-
- Article
-
- You have access
- Export citation
-
We prove that, given a positive integer
$m$, there is a sequence 
$\{n_{i}\}_{i=1}^{k}$ of positive integers such that with the property that partial sums of the series
$$\begin{eqnarray}m=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\cdots +\frac{1}{n_{k}}\end{eqnarray}$$
$\{1/n_{i}\}_{i=1}^{k}$ do not represent other integers.
