Question 59
Prove that among any $20$ consecutive positive integers there exists a number $d$ such that for each positive integer $n$ we have the inequality
$$
n\sqrt{d}\{n\sqrt{d}\} \gt \frac{5}{2}
$$
where $\{x\}$ denotes the fractional part of the real number $x$.
$$
n\sqrt{d}\{n\sqrt{d}\} \gt \frac{5}{2}
$$
where $\{x\}$ denotes the fractional part of the real number $x$.