Question 32
Let $n$ be a positive integer not divisible by $3$. Prove that $n$ admits a representation of the form:
$$
n = \frac{3xy}{x+y}
$$
where $x$, $y$ are positive integers,
if and only if $n$ has at least one divisor of the form $3k+2$ for some $k = 0,1,2,...$.
$$
n = \frac{3xy}{x+y}
$$
where $x$, $y$ are positive integers,
if and only if $n$ has at least one divisor of the form $3k+2$ for some $k = 0,1,2,...$.