The Binary RootAlgebra Level 5
A quadratic equation
is called binary-quadratic if it satisfy the following conditions:
All digits of the non-negative integers \(p\) and \(q\) are either \(0\) or \(1\)
All digits of the roots are either \(0\) or \(1\)
How many binary-quadratic equations are there such that both roots are smaller than \(10^4\).