ROSECODE 141
Lattice points
For a,b,c,d all being positive integers, we have the following:
L1: y=(b/a)*x
L2: y=-(a/b)*x+a
L1 and L2 cross at a P(c,d) point.
The distances from P to origin (0,0) and to (0,a) and to (b,0) points are all integers.
Let f(R) denote the number of (a,b,c,d) solutions if P is inside x^2+y^2=R^2 circle.
You are given:
f(10^5)=3782
What is f(10^19)?
[My timing: <100ms]
L1: y=(b/a)*x
L2: y=-(a/b)*x+a
L1 and L2 cross at a P(c,d) point.
The distances from P to origin (0,0) and to (0,a) and to (b,0) points are all integers.
Let f(R) denote the number of (a,b,c,d) solutions if P is inside x^2+y^2=R^2 circle.
You are given:
f(10^5)=3782
What is f(10^19)?
[My timing: <100ms]