Show that one and only one out of n, n+2 or n+4 is divisible by 3, where n is any positive integer.
Asked by rajadeepakkumar | 20th Nov, 2009, 08:23: PM
Let the three consecutive integers be n, n+2 and (n+4).
We can write n + 4 = (n+1) + 3, 3 is any ways divisible by 3.
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 i.e (n+4) 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 | 24th Nov, 2009, 09:44: AM
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