SOLUTION: Show that if x^2 is odd, x is odd. Use proof by contradiction.

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Question 992554: Show that if x^2 is odd, x is odd. Use proof by contradiction.
Answer by ikleyn(52803) About Me  (Show Source):
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Show that if x^2 is odd, x is odd. Use proof by contradiction.
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We are given that  x%5E2  is odd.
We need to prove that  x  is odd.

Let us assume that  x  is not odd.  Then  x  is even.  In other words,  x  is divisible by  2.  Hence,  x = 2n,  where  n  is integer.

Then  x%5E2 = %282n%29%5E2 = 4n%5E2  is even.

This contradicts to the fact that  x%5E2%26  is odd,  which is given.

The source of the contradiction is the assumption that  x  is not odd.

Hence,  x  is odd.

The proof is completed.