# ordered of pairs

• Dec 7th 2011, 10:41 AM
sri340
ordered of pairs
In 1953, L.J.Mordell said that there were only four ordered triples of integers (x, y, z) for which x^3 +y^3 +z^3 = 3 .one of these is (1, 1, 1). What are the other three ordered triples?
• Dec 7th 2011, 11:03 AM
TheChaz
Re: ordered of pairs
(4, 4, -5)
(4, -5, 4)
(-5, 4, 4)
• Dec 7th 2011, 11:33 AM
sri340
Re: ordered of pairs
can you give me explanation
• Dec 7th 2011, 11:39 AM
TheChaz
Re: ordered of pairs
I thought that I could answer it.
I assumed, since the claim was that there were exactly three more solutions, and since the equation is symmetric in x/y/z, that the solutions would be symmetric.
I assumed that two of the variables were equal.
I tried a few smaller numbers, and considered powers of small numbers.
I came across the given solution.
I typed in into the box, and hit "Post quick reply".
• Dec 7th 2011, 12:02 PM
HallsofIvy
Re: ordered of pairs
Good Explanation!
• Dec 7th 2011, 12:05 PM
TheChaz
Re: ordered of pairs
Quote:

Originally Posted by HallsofIvy
Good Explanation!

It probably won't earn me the "Best MHF Helper 2011" award...

If anything, I'd like to see a little more confidence and effort in the world :)