CONO-SUR 2016 Problem 6

We say that three different integers are friendly if one of them divides the product of the other two. Let $n$ be a positive integer.

a) Show that, between $n^2$ and $n^2+n$ , exclusive, does not exist any triplet of friendly numbers.

b) Determine if for each $n$ exists a triplet of friendly numbers between $n^2$ and $n^2+n+3\sqrt{n}$ , exclusive.