Prove that any number of the form 4n+2 can never be a perfect square.

Asked by mehaksaini | 4th Feb, 2010, 11:17: AM

Expert Answer:

4n+2=2(2n+1)

where n is a natural number.

 so then, 2n+1  will be an odd number.

 so it won't have 2 as a factor.

 so 2(2n+1) will not have all factors which are repeated, which is necessary for 4n+2 to be a perfect square.

 hence the answer.

Answered by  | 5th Feb, 2010, 07:03: PM

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