# Problem 420: 2x2 positive integer matrix

![graphic](img420.gif)

A positive integer matrix is a matrix whose elements are all positive
integers. Some positive integer matrices can be expressed as a square of
a positive integer matrix in two different ways. Here is an example: We
define F(N) as the number of the 2x2 positive integer matrices which
have a trace less than N and which can be expressed as a square of a
positive integer matrix in two different ways. We can verify that F(50)
= 7 and F(1000) = 1019. Find F(107).