Number theory- prove no three ppt's with same value c

[RossH]

Homework Statement

The problem is that I have to prove that there aren't three or more primitive pythagorean triples with the same value of c. A primitive pythagorean triple has has no values, a, b, or c that have common factors.
The actual question is if this is possible, and if not prove it.

Homework Equations

Of course you know that a pythagorean triple fulfills the equation a²+b²=c².
I am pretty sure that a relevant equation is the way to find pythagorean triples: a=st, b=(s²-t²)/2 c=(s²+t²)/2 for any s and to such that the above all are whole numbers.

The Attempt at a Solution

So far I have just been manipulating the various variables that I have above. I am trying to do a proof by contradiction, perhaps by creating a system of equations and showing that two of the triples must be identical, but all that I have managed to prove so far is that 0=0, which isn't exactly useful. I don't really know where to start if this isn't the right approach.

Thanks!

 

[Dick]

You can't prove that. Because it's not true. I'm not sure how you are expected to discover it's not true. Any idea?

 

[RossH]

You can't prove that. Because it's not true. I'm not sure how you are expected to discover it's not true. Any idea?

Oops. Yeah, I just found a few triples. Thanks. I'm handing in the assignment tomorrow so I'll post back here what my professor says about that question.

 

[lifom]

I use computer to compute from 1 to 1000, I still can't find 3 different ppts with same values of c. Can you give me an example?

 

[Dick]

I use computer to compute from 1 to 1000, I still can't find 3 different ppts with same values of c. Can you give me an example?

I don't think you went quite far enough. Try 1105. And look at http://www.math.rutgers.edu/~erowland/pythagoreantriples.html