n & n - 1 are two consecutive numbers which means one of is surely even and the other one is odd.
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Suppose that n is an even number;
So we can right n like this :
n = 2t
Thus :
n - 1 = 2t - 1
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n( n - 1 ) = 2t( 2t - 1 ) = 2 ( 2t^2 - t )
= 2 ( q ) = 2q
The number obtained is a multiple of 2, so it is definitely even because all numbers are even multiples of 2.
