Question 169
For any real number $p \ge 1$ let us consider the set of all real numbers $x$ with
$$
p \lt x \lt \left(2 + \sqrt{p + \frac{1}{4}}\right)^2
$$
Prove that from such a given set one can select four mutually different natural numbers $a, b, c, d$ with $ab = cd$.
$$
p \lt x \lt \left(2 + \sqrt{p + \frac{1}{4}}\right)^2
$$
Prove that from such a given set one can select four mutually different natural numbers $a, b, c, d$ with $ab = cd$.