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Question 242614: Prove that no number of the type 4k+2 be a perfect square.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Prove that no number of the type 4k+2 can be a perfect square.
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Lemma:
If p is a prime factor of a perfect square, p^2 must also
be a factor of that perfect square.
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4k+2 = 2(2k+1)
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2 is a factor of 4k+2 but 2k+1 is odd and cannot have factor 2, so 4k+2 is not divisible by 4, and therefore cannot be a perfect square.
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Edwin
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