At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

just use gaussian elimination

oh.... I have bad eyes

I don't think so....

There are four variables, only two equations, but the answer sets have to be integers.

They call that a Diophantine equation, right?

You're probably off track!

lol

not very optimistic

I think the Z^4 is a hint

pretty interesting question

wolfram's answer was not very comforting :/

lol yea turning test

let's write a Python script to solve this.

or maybe a calculator program?

If someone finds the answer using software, please don't post it yet!

but if I could write such programs... then maybe I would be able to do this by hand :-P

what exactly is the Diophantine equation?

but then we could write a dynamic programming solution!

http://en.wikipedia.org/wiki/Diophantine_equation

um so how do we implement that here?? i am not getting any clue from that

beats me, I'm just thinking out loud...

As we say R for real number x, and R^2 for the plane (x,y) and so on.

I like how the 4th dimension is time

ahhh... thank you, that is insightful :)

why did u take y=0? i didnt get that?

For the case \(t=0\), we will have \(y=z=1\) and \(x=3\). Thus the solution \((3,1,10)\).

ok yea now i am getting it

A typo! The last solution is \((3,1,1,0)\).

I know, so taking x=0 gave
yt=-3/2
so that means no integer solutions when x=0, right?

Exactly!

Okay,
I'm getting the picture, thanks!

so it looks like the only easy solutions are the ones you posted, but are there more?

I can't say! We haven't showed that these are the only solutions, assuming that's true.

I can say there are no solutions for \(x=y=z=t, x=y, \text{ or } t=z\).

I see it for t=z

Plug \(x=y=z=t\), you get \(x^2-2x^2=3\), which has no solution even over R.

x or z cannot be 0

Correct at Pax.

I can't see that by looking at it, maybe I'm missing it.

the fact that the above has no integer solutions I mean

For some reason, I feel those two solutions are the only solution. But I can't prove it!

Likewise...

solutions*

Zarkon has it I think! :D

We've at least proved that those are the only solution in the case that either y or t are zero.

all I got so far is the x & z have to be odd (y,t!=0):\[yt={xz-3 \over 2}\]

look above Pax, we have more than that

We've also proved, for several cases, that no integer solutions exist. Yet, that is not enough.

I believe I have a similar argument for y<0 and z>0

note in the above argument that y>1 is the same as \(y\ge 2\) and z>0 is the same as \(z\ge 1\)

so just 4 solution sets...

Wow, you guys are amaaaaazing!!!! I'm totally impressed.

Not that amazing! I was stupid enough to not notice that x=z=-1 is an integer solution for xz=1. ;)

It was a nice problem. Of course, only Zarkon proved that only four solutions are there! :D