SOLUTION: Does 3 divide(3k+1)(3k+2)(3k+3)?

Question 860312: Does 3 divide(3k+1)(3k+2)(3k+3)?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
note for n, d elements of Z and d is not = 0, then n is divisible by d if and only if, n = d * k for some k in Z.
now
Does 3 divide(3k+1)(3k+2)(3k+3)? YES
Proof
(3k + 1)(3k + 2)(3k + 3) = 3(3k + 1)(3k + 2)(k + 1)
since k is an element of Z, it follows that (3k + 1)(3k + 2)(k + 1) is an element in Z, this and our definition of divisible gives us the desired result.

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