by mithunsam Mon Aug 08, 2011 10:03 am
Statement 1 -> n^2-2n is not a multiple of 4
If n is even (E), then the equation will become E^2 -2E
=E*E - 2*E
But, 2 is a prime factor for every even. So, we can write E = 2*x, where x is any number
So the equation becomes (2*x)*(2*x) - 2*(2*x) = 4x^2-4x=4(x^2-x). This is a multiple of 4.
Therefore, if n is even, then n^2-2n will be a multiple of 4. But statement states that n^2-2n is not a multiple of 4. Hence, n is not even (otherwise, n is odd).
Note to Jeff (n=2 or n=0 will make n^2-2n = 0. However, 0 is a multiple of every number. So n cannot be either of these two values)
Last edited by
mithunsam on Thu Aug 18, 2011 1:14 pm, edited 1 time in total.