pls help

Asked by  | 11th Mar, 2009, 12:21: PM

Expert Answer:

We know that themultiples of 3 will differ by 3. Also every multiple of 3 is either an odd number or an even number. Suppose out of the given numbers  n,n+2,n+4 If n is a multiple of 3, there's nothing more to prove. So, let's assume that  n is not a multiple of 3. Then n-3 is not a multiple of 3, so either n-1, or n-2 must be a multiple of 3. So next multiple of 3 would be either (n-1)+3= n+2 or (n-2)+3 =n+1 So we see that if n is not a multiple of 3 then n+2 may be a multiple of 3 or n+1 may be a multiple of 3  Next, if n+1 is a multiple of 3 , then (n+1)+3 must be a multiple of 3 i.e. n+4 must be a multiple of 3. So we see that if n is not a multiple of 3 then either n+2 or n+4 is a multiple of 3. Thus either of n, n+2 or n+4 is always a multiple of 3. i.e. one out of n,n+2 or n+4 is divisible by 3.

Aswered by  | 11th Mar, 2009, 01:20: PM

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