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

  • Thread starter RossH
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  • #1
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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

  • #2
Dick
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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?
 
  • #3
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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.
 
  • #4
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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?
 
  • #5
Dick
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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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