Question 7
For any real number $t$, denote by $[t]$ the greatest integer which is less than or equal to $t$. For example: $[8]=8$, $[\pi]=3$ and $[-5 / 2]=-3$. Show that the equation
$$
[x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345
$$
has no real solution.
$$
[x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345
$$
has no real solution.