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 March 29th, 2018, 10:45 AM #1 Newbie   Joined: Mar 2018 From: California Posts: 18 Thanks: 0 Yet another problem 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.
 March 29th, 2018, 12:20 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 (7,15,20) and (15,7,20)
March 29th, 2018, 01:13 PM   #3
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Quote:
 Originally Posted by Denis (7,15,20) and (15,7,20)
Could you explain how you arrived at these answers?

 March 29th, 2018, 02:12 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Wrote short looper program.
March 29th, 2018, 03:04 PM   #5
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Quote:
 Originally Posted by Denis 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?

 March 29th, 2018, 03:23 PM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 It's simply hit and miss...brute force. No "solving" involved.
March 29th, 2018, 04:31 PM   #7
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Quote:
 Originally Posted by Denis 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?

 March 29th, 2018, 05:03 PM #8 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,299 Thanks: 960 Math Focus: Wibbly wobbly timey-wimey stuff. 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 Thanks from Denis
 March 29th, 2018, 05:32 PM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Agree. That's exactly what I did; from 1 to 999. Thanks from topsquark
March 29th, 2018, 05:37 PM   #10
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Quote:
 Originally Posted by Denis 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?

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