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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 a

^{2}+b

^{2}=c

^{2}.

I am pretty sure that a relevant equation is the way to find pythagorean triples: a=st, b=(s

^{2}-t

^{2})/2 c=(s

^{2}+t

^{2})/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!