SOLUTION: Can you help me solve (Given: n is odd )(Prove: n^2 is odd)

Question 168296: Can you help me solve (Given: n is odd )(Prove: n^2 is odd)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Can you help me solve (Given: n is odd )(Prove: n^2 is odd)
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If n is odd, n = 2x+1 where x is an integer.
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Then n^2 = (2x+1)^2 = 4x^2+4x + 1 = 2(2x^2+2x) +1
Since x is an integer, 2x^2+2x is an integer.
So, 2(2x^2+2x)+1 follows the form 2(integer)+1
So (2x+1)^2 is odd.
Therefore n^2 is odd.
Cheers,
Stan H.
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