Question

Sorry, I misphrased the question earlier. What are the four ordered pairs of integers (x , y , z) for which x^3 + y^3 + z^3 = 3?

Answer 1

1 works

Answer 2

It has to be an ordered pair.

Answer 3

(x,y,z) is not an ordered pair

Answer 4

Lol. My bad. I meant ordered triple.

Answer 5

(4,4,-5)

Answer 6

i like my answer too.

Answer 7

i like zarkon's because it seems more sophisticated

Answer 8

jk
i like your answer too satellite

Answer 9

i have do doubt that zarkon's answer is more sophisticated. a more interesting question is how many such ordered pairs there are

Answer 10

(4,-5,4)
(-5,4,4)
are two others lol

Answer 11

cheater

Answer 12

its only cheating if it looks exactly the same

Answer 13

did you get that line from your students?

Answer 14

One last one ... lol.

Answer 15

yes i learn from them

Answer 16

you have your 4

Answer 17

A tougher question is proving there are only 4.

Answer 18

can you prove that james?

Answer 19

or how would you go about proving it

Answer 20

Not quickly, no.

Answer 21

i should say not
http://mathoverflow.net/questions/58188/are-nontrivial-integer-solutions-known-for-x3y3z33

Answer 22

If I'd taken number theory sometime in the last decade I could tell you how to approach proving it. But a problem like this is either easy or absurdly hard.

Answer 23

let's assume it is absurdly hard and call it a day ;)

Answer 24

@sat73. Ha, yes. It belongs to the 'absurdly hard' category.

Answer 25

"Of course the problem is old and probably there is no hope to be resolved." i'll get back to you after lunch

Answer 26

Lol ... I can't do proofs.

Answer 27

Anyway ... what's the other question CentSci?

Answer 28

ok lets not worry about it
lets not get headaches

Answer 29

Nothing ... I think you got all the triples.

Answer 30

ok