## Proof Exercise #1 Continuation 7

Yes.

Therefore, 2v^2 = (2k)^2.

Therefore 2v^2 = 4k^2.

Therefore v^2 = 2k^2.

Therefore:

choice #1: 2 is a divisor of v^2.

choice #2: 2 is an odd prime.

choice #3: 3 is an even prime.

choice #4: Every divisor of 2 is a divisor of 3.

choice #5: v^2 is a divisor of a prime.

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Therefore, 2v^2 = (2k)^2.

Therefore 2v^2 = 4k^2.

Therefore v^2 = 2k^2.

Therefore:

choice #1: 2 is a divisor of v^2.

choice #2: 2 is an odd prime.

choice #3: 3 is an even prime.

choice #4: Every divisor of 2 is a divisor of 3.

choice #5: v^2 is a divisor of a prime.

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