- #1
Animuo
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Homework Statement
Prove by Contradiction: For all Prime Numbers a, b, and c, a^2 + b^2 =/= c^2
Homework 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.
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
Rearrange it:
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!