I'm trying to prove rigorously the following:
$\lfloor x/a/b \rfloor$ = $\lfloor \lfloor x/a \rfloor /b \rfloor$ for $a,b>1$
So far I haven't gotten far. It's enough to prove this instead
$\lfloor z/c \rfloor$ = $\lfloor \lfloor z \rfloor /c \rfloor$ for $c>1$
since we can just put $z=\lfloor x/a \rfloor$ and $c=b$.