Question 76
Let $n$ be a positive integer. Prove that the interval
$$
I_{n} = \left( \frac{1 + \sqrt{8n + 1}}{2}, \frac{1 + \sqrt{8n + 9}}{2} \right)
$$
does not contain any integer.
$$
I_{n} = \left( \frac{1 + \sqrt{8n + 1}}{2}, \frac{1 + \sqrt{8n + 9}}{2} \right)
$$
does not contain any integer.