MathDB

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.

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