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# Even/Odd Question

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Senior Manager
Joined: 25 Mar 2009
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21 Jun 2009, 11:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

(k+1)(k+2)(k+3)

In the above expression, if k is ODD, then (k+1) is EVEN, (k+2) is ODD, & (k+3) is EVEN. The product of all 3 is an EVEN number.

My question: Is (k+1)(k+2)(k+3) divisible by 4? How do you know it is or is not?
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21 Jun 2009, 12:04
1
KUDOS
Expert's post
topher wrote:
(k+1)(k+2)(k+3)

In the above expression, if k is ODD, then (k+1) is EVEN, (k+2) is ODD, & (k+3) is EVEN. The product of all 3 is an EVEN number.

My question: Is (k+1)(k+2)(k+3) divisible by 4? How do you know it is or is not?

You can't be certain it's divisible by 4 - it may be, and it may not be:

If k is odd, then both k+1 and k+3 will be even, and when you multiply two even numbers, you always get a multiple of 4. So if k is odd, then the product will certainly be a multiple of 4.

If k is even, then k+2 is the only even number in the product. If k+2 is divisible by 4, the product will be; if, on the other hand, k+2 is not divisible by 4, then the product will not be divisible by 4. Even numbers alternate between multiples of 4 and non-multiples of 4; if k is divisible by 4, k+2 is not.

Combining the above, we have: The product (k+1)(k+2)(k+3) will be divisible by 4 if and only if k is *not* divisible by 4.
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Senior Manager
Joined: 25 Mar 2009
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21 Jun 2009, 13:27
Perfect explanation. I get it now. Thank you.
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23 Jun 2009, 11:18
If you have a (k+4) then it will be, otherwise it's CBD
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Re: Even/Odd Question   [#permalink] 23 Jun 2009, 11:18
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# Even/Odd Question

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