Project Euler Problem 397

On the parabola y = x^2/k, three points A(a, a^2/k), B(b, b^2/k) and C(c, c^2/k) are chosen.

Project Euler Problem 397

Solution

Answer: 141630459461893728

Let

$$ P(t)=\left(t,\frac{t^2}{k}\right) $$

and define

$$ A=P(a),\qquad B=P(b),\qquad C=P(c), $$

with

$$ -X\le a<b<c\le X,\qquad 1\le k\le K. $$

We must count all9 $$ gives $$ F(10^6,10^9)=141630459461893728. $$ citeturn0search