Question 70
For a real number $x$, let $[x]$ denote the greatest integer not exceeding $x$.
a. Prove that for all positive integers $a,b,c$,
$$\left[\frac{[c/a]}b\right]=\left[\frac c{ab}\right].$$
b. Give an example showing that this equality does not hold for all positive real numbers $a,b,c$.
a. Prove that for all positive integers $a,b,c$,
$$\left[\frac{[c/a]}b\right]=\left[\frac c{ab}\right].$$
b. Give an example showing that this equality does not hold for all positive real numbers $a,b,c$.