I am assuming the expression is n(n+1)(n+2)
a) This not true. If n is even, (n+1) will be odd and if n is odd (n+1) will be even. It is sufficient for any one of the terms to be even to make the entire expression even.
b) For the same reasons as "a" this is alos not true.
c) This is also not true. It is sufficient for (n+1) alone to be a multiple of 3 for the entire expression to be divisible by 3. eg : n=2
e) Whenever n is even, (n+2) will also be even. Hence the expression will have two even integers and hence is always divisible by 4.
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