Question 41
Let $\alpha$ and $\beta$ be two positive integers. Prove that the integer
$$
\alpha^2 + \left\lceil \frac{4\alpha^2}{\beta} \right\rceil
$$
is not a square of an integer.
$$
\alpha^2 + \left\lceil \frac{4\alpha^2}{\beta} \right\rceil
$$
is not a square of an integer.