yaworsw/euler-manager

---
:id: 420
:name: 2x2 positive integer matrix
:url: https://projecteuler.net/problem=420
:content: "A _positive integer matrix_ is a matrix whose elements are all positive
  integers.  \nSome positive integer matrices can be expressed as a square of a positive
  integer matrix in two different ways. Here is an example:\n\n ![p420_matrix.gif]({{
  images_dir }}/p420_matrix.gif)\n\nWe define F(<var>N</var>) as the number of the
  2x2 positive integer matrices which have a <dfn title=\"the sum of the elements
  on the main diagonal\">trace</dfn> less than <var>N</var> and which can be expressed
  as a square of a positive integer matrix in two different ways.  \nWe can verify
  that F(50) = 7 and F(1000) = 1019.\n\nFind F(10<sup>7</sup>).\n\n"