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Show that one and only out of n; + 2 or n + 4 is divisible by 3, where is any positive integer.

Show that one and only out of n; + 2 or n + 4 is divisible by 3, where is any positive integer.

Grade:

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
let n is divisible by 3 hence n=3k
so n+2=3k+2,n+4=3(k+1)+1 are not divisible by 3
similarly if n+2=3k
so n=3k-2 and n+4=3k+2 are not divisible by 3
similarly if n+4=3k
so n=3(k-1)-1 and n+2=3k-2 are not divisible by 3
Hence only one out of n,n+2,n+4is divisible by 3
mycroft holmes
272 Points
6 years ago
If n and (n+2) are divisible by 3, then so is their difference 2.
 
Similarly you can argue for the pairs (n,n+4) and (n+2,n+4)

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