If value of $a+b+c$ is given as $n$ and it is provided that a2+b2 = c2. So, I need to find the value of $(abc)$ in terms of $n$.
closed as off-topic by Dietrich Burde, user91500, José Carlos Santos, Shaun, Antonios-Alexandros Robotis Aug 9 '17 at 10:10
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user91500, Shaun, Antonios-Alexandros Robotis
You can't hope for an answer in general, because two equations in three variables will generally give a one dimensional set of points. But the answer can sometimes be given in terms of a single parameter. Here it is easy enough to work through:
the points $(x,y,z)$ with $x^2+y^2=z^2$ form an infinite cone in the $x,y,z$ plane.
The points $(x,y,z)$ with $x+y+z=\alpha$ form a plane. The intersection of the plane and the cone is a conic.
This conic can contain a large number of lattice points.