show that one of 3 consecutive integers is divisible by 3

Asked by  | 9th Mar, 2009, 10:02: AM

Expert Answer:

Let the three consecutive integers be n, n+1 and n+2

Case1: n is divisible by 3. Then we are done

Case2: n is not divisible by 3.

Then the number is a multiple of a prime number other than 3. Adding 1 or 2 to any such number will make it divisible by 3.

If adding 1 makes it divisible by 3, then n+1 is divisible by 3.

If adding 2 makes it divisible by 3, then n+2 is divisible by 3.

Hence we are done.

Answered by  | 9th Mar, 2009, 11:42: AM

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