Hi guys,First of all please pardon my language , I'm from Italy and not fluent in english.

I discoverd a mathematical problem in a book which made me curious: It's about matrices but goes beyond the basic calculation that I'm used to.

We look at the set of 2 x 2 matrices made out of natural numbers only.

Some of these matrices have "squareroots" , i.e. there is some certain 2 x 2 matrix which, multiplicated by itself, gives our original 2 x 2 matrix. The quantity of these square-roots is different from matrix to matrix.

So the question is: What's the quantity of 2 x 2 matrices (filled with natural number, no 0 allowed) which have 2 squareroots AND whose trace is not larger than x.

For example x = 1.000

Any Ideas ?