# Yet another problem

#### MathDude666

Solve in positive integers
$x^3 + y^3 +3xyz = z^3 + 2018$

This problem doesn't seem to be solvable because there are three variables in one equation. Could anyone provide some assistance? Full solutions are appreciated with justifications.

#### Denis

Math Team
(7,15,20) and (15,7,20)

#### MathDude666

(7,15,20) and (15,7,20)
Could you explain how you arrived at these answers?

#### Denis

Math Team
Wrote short looper program.

#### MathDude666

Wrote short looper program.
Could you explain how the looper program computes the values for x y and z? Like what stops is it taking?

#### Denis

Math Team
It's simply hit and miss...brute force.
No "solving" involved.

#### MathDude666

It's simply hit and miss...brute force.
No "solving" involved.
Then how did you bash out and get those specific solutions? What kinds of numbers were you looking for?

#### topsquark

Math Team
I would say that you simply do three loops: x, y, z from 1 to 50 and check to see if the x,y,z values work. Nothing too complicated. (You can also be crafty and note that if x, y, z is a solution, then so is y, x, z.)

-Dan

• 1 person

#### Denis

Math Team
Agree. That's exactly what I did; from 1 to 999.

• 1 person

#### MathDude666

Agree. That's exactly what I did; from 1 to 999.
So you created like a computer program to do so? Or bash them all out by hand?