*Problem #109*

Consider the *n*^{2} expressions

for integers *a*, *b*, where 1 ≤ *a*,*b* ≤ *n*.
Let *f*(*n*) be the number
of these expressions that are identical to some expression
of the form
where *x*, *y*, and *z* are positive
integers. What is the asymptotic behavior of *f*(*n*)?
That is, find a simple function *g*(*n*) so that
**Source:John T. Robinson of Yorktown Heights, NY**

**
The solution will be posted shortly.
**

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