Problem #109

Consider the n2 expressions

for integers a, b, where 1 ≤ a,bn. 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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