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.
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.