Question 8
We say that three positive integers $a$, $b$, $c$ form a *family* if the following two conditions hold:
$$
\bullet\ a+b+c=900;
$$
• there exists an integer $n$, $n \ge 2$, such that $\frac{a}{n-1} = \frac{b}{n} = \frac{c}{n+1}$.
Find the number of families.
$$
\bullet\ a+b+c=900;
$$
• there exists an integer $n$, $n \ge 2$, such that $\frac{a}{n-1} = \frac{b}{n} = \frac{c}{n+1}$.
Find the number of families.