SOLUTION: please help me solve this question: show that 4 does not divide (n^2+2) for any n

Question 769172: please help me solve this question: show that 4 does not divide (n^2+2) for any n
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Need to show that (n^2 + 2)/4 is not an integer
For n odd, n^2 is always odd -> n^2 + 2 is always odd. An odd number does not divide evenly by 4.
(n^2 + 2)/4 = n^2/4 + 1/2
For n even, n^2/4 will always give an integer value
This is because an even number can be written as a multiple of 2, i.e. 2k
n^2/4 = 4k^2/4 = k^2 = integer for all values of k
An integer + 1/2 is not a whole number, so it does not divide evenly for even values of n

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