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

## 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!

## Answers and Replies

Dick
Science Advisor
Homework Helper
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?

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.

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
Science Advisor
Homework Helper
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 [Broken]

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