Question 45
We say a rational number is good if it can be written as $\frac{a}{b} + \frac{b}{a}$ for some positive integers $a$ and $b$.
(i) Show that any integer $n \ge 4$ can be written as the sum of some good numbers.
(ii) What is the minimum number of good numbers that $n = 57$ can be written as the sum?
(i) Show that any integer $n \ge 4$ can be written as the sum of some good numbers.
(ii) What is the minimum number of good numbers that $n = 57$ can be written as the sum?