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April 7th, 2014, 08:38 PM   #1
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Matrices problem

Lira loves Linear Algebra and she is especially keen about matrix .

Today, she learnt some properties about matrices, namely, she learnt about what the trace of a matrix is, as her teacher gave her many exercises for her to practice.

As we know she is pretty clever, she rapidly came up with some definitions of her own and devised a somewhat harder version of the problem initially proposed by her teacher.

Namely, she defines a Positive Invertible Integer Matrix as being an invertible 2x2 matrix composed only of positive (i.e. greater than 0) integer elements and whose determinant is greater than 0.

Now, she is interested in counting how many such matrices are there, such that their trace is equal to N .

i tried to solve problem but the computer program takes 10 sec for N=2500.any short way to solve this problem ?
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