Question 19
a. Prove that if $n$ is a positive integer such that $n \geq 4011^{2}$, then there exists an integer $l$ such that $n \lt l^{2} \lt \left(1 + \frac{1}{2005}\right) n$.
b. Find the smallest positive integer $M$ for which whenever an integer $n$ is such that $n \geq M$, there exists an integer $l$, such that $n \lt l^{2} \lt \left(1 + \frac{1}{2005}\right) n$.
b. Find the smallest positive integer $M$ for which whenever an integer $n$ is such that $n \geq M$, there exists an integer $l$, such that $n \lt l^{2} \lt \left(1 + \frac{1}{2005}\right) n$.