Given that E, K, m > 0, then is there a way to find out value of m in terms of E and K for
$$\left\lfloor\frac{E}{K} \right\rfloor =\left\lfloor \frac{E}{K + m} \right\rfloor$$
All I have gotten so far is this:
$$ \frac{E}{K}-1 \lt \left\lfloor\frac{E}{K}\right\rfloor \le \frac{E}{K} $$
and,
$$ \frac{E}{K+m}-1 \lt \left\lfloor\frac{E}{K+m}\right\rfloor \le \frac{E}{K+m} $$
and since $\left\lfloor\frac{E}{K} \right\rfloor =\left\lfloor \frac{E}{K + m} \right\rfloor$,
$$ \implies \frac{E}{K}-1 < \frac{E}{K + m} $$
leading to,
$$ m < \frac{K^2}{E - K} $$
but I am looking for a tighter bound, preferably in terms of equality. Any help will be greatly appreciated.
Edit: I forgot to add that $ E \gt K $