Question 182
Find all the natural numbers $n$ that check the condition: $$
\left[\frac{n}{2}\right]+\left[\frac{2 n}{3}\right]=n+335
$$ where $[x]$ is the integer part of $x$. (that is, $[1,32]=1$, $[2]=2$, $\left[\frac{1}{2}\right]=0$, $[\pi]=3$, etc.)
\left[\frac{n}{2}\right]+\left[\frac{2 n}{3}\right]=n+335
$$ where $[x]$ is the integer part of $x$. (that is, $[1,32]=1$, $[2]=2$, $\left[\frac{1}{2}\right]=0$, $[\pi]=3$, etc.)