Thread: Equation

which points satisfies the problem below?

Originally Posted by streethot

which points satisfies the problem below?

x = 0
y = 0
z = 9

you have gave a particular solution... now, you have to prove that this is the only solution

Originally Posted by streethot

you have gave a particular solution... now, you have to prove that this is the only solution

Lol! I'm not here to do your homework for you.

You merely asked for a point that satisfied the equation, and I gave you one.

If you want help with proving or otherwise that there's only one unique solution, then that's a different equation.

Ah, how the road to mathematical truth is paved in blood...

streethot:

There are more solutions than you should care to count. A simple calculator program can tell you that...

1,-1,-1
1,-1,0
1,-1,1
-1,2,2
0,2,1
1,-1,-2
1,-1,2
-1,3,1
0,1,3
0,3,0
etcetera ad nauseam

As you know, Diophantine equations are notoriously difficult to solve. There may be an infinite number of solutions readily found by number-crunching.

What exactly is it that you want to know about this equation? A proof of whether or not there is an infinitude of points? A formula generating a set of solutions?

Thank you Media_Man. I was thinking that could have a way to solve this problem by the same method used to solve this:



A classmate proposed this problem to me, i will investigate. Anyway, thanks for help me

Here's a small part:

If you rearrange the equation you'll get the following:



When X=1, and Y=-1 we get , in other words

So, any Z will work for X=1 and Y=-1


Some other brute force stuff:
When you set one variable to equal zero, there's only a finite number of solutions that will work (tried for X = 0 and Z = 0, Y = 0 will probably behave the same way)

I don't think there's one general formula for the solution though, because of the (1,-1,Z) case ...

Now i know what is the real question.

Is for

Originally Posted by streethot

Now i know what is the real question.

Is for

Indeed, it is a diophantine equation.

After much work, i got it! i will post with more calm after because the solution is a little long.