|Aug1-12, 11:38 AM||#1|
Prove by Contradiction: For all Prime Numbers a, b, and c ..
1. The problem statement, all variables and given/known data
Prove by Contradiction: For all Prime Numbers a, b, and c, a^2 + b^2 =/= c^2
2. Relevant equations
Prime number is a number whose only factors are one and itself.
Proof by contradiction means that you take a statement's negation as a starting point, and find a contradiction.
3. The attempt at a solution
The statement's negation is:
There exists prime numbers a, b, and c, such that a^2 + b^2 = c^2
a^2 = c^2 - b^2
a^2 = (c - b) (c + b)
a = √(c-b)(c+b)
I'm stuck here. To show that it's a contradiction I would have to show that it's factors are not equal to 1 or a, and I've been staring at this a little too long, my head just keeps going in circles.. some help would be appreciated!
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