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c. Let a, b, c denote a primitive Pythagorean triple. Using cases and proof by contradiction. prove that exactly one of a, b, c is even. You may use without proof that an even number plus an odd number is odd, etc. (Note: We used something stronger in class, that exactly one of a, b is even. I think this is harder to prove and requires modular arithmetic, which we will see later in the class.)
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