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- Mon Apr 19, 2021 7:56 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO Secondary National 2021 #3
- Replies: 5
- Views: 7847
Re: BDMO Secondary National 2021 #3
\begin{align*} &25\left\{r\right\}+\left[r\right]=125\\ \Rightarrow&25\left\{r\right\}=125-\left[r\right] \end{align*} As $125-\left[r\right]$ is an integer, $25\left\{r\right\}$ must be an integer too. If $\left\{r\right\}=0$, then $r=125$. Otherwise, suppose $\left\{r\right\}=\dfrac{p}{q}$ where ...