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Question 286032: prove that no number of the type 4k+2 be a perfect square.
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! Denote a^2=4k+2=2(2k+1). So 2|a^2 thus 2|a. Let a=2n. Then a^2=4n^2 which means 4|a^2.
However, we have a^2=4k+2. 4 does not divide 4k+2, hence 4k+2 can never be a perfect square.
In other words: if a is even, its square will always be divisible by 4.
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