Question

prove that one and only one out of n,(n +1),(n +2) is divisible by 3.where n is any positive integer.​

Answer 1

Answer:

Since n, n+1, n+2 are three consecutive integers then there must be one number divisible by 3 at least. 

If the remainder at dividing n by 3 is 1, then n+2 must be divisible by 3 and if the remainder at dividing n by 3 is 2, then n+1 must be divisible by 3. Similarly for n+1 and n+2.

Let n be divisible by 3.

3n+1=3n+31

Now, n is divisible by 3 but 1 is not. So we get n+1 not divisible by 3. Similarly,n+2 will not be divisible by 3 as well if n is divisible by 3.

3n+2=3n+32

In the same way, if n+1 is divisible by 3 then n and n+2 can't be divisible by 3. If n+2 is divisible by 3 then n and n+1 cannot be divisible by 3.

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