Question

show that one and only one out of n,n+2 or n+4 is djvisible by 3 where n is any positive integer

Answer 1

Hi,
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Here is your answer,
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On dividing n by 3, let q be the quotient and r be the remainder.
Then, n= 3q+r
=> n= 3q+r
=> n= 3q or n= 3q+1 or n= 3q+2 .
Case I. If n=3q , then n is divisible by 3 .
Case ll. If n=3q+1 then (n+2)= 3q+3 = 3(q+1), which is divisible by 3.
So, in this case (n+2 ) is divisible by 3.
Case lll. when n= 3q+2 then (n+4)=3q+6=3(q+2), which is divisible by 3.
So, in this case (n+4) is divisible by 3.
Hence, one and only one out of n, n+2 , n+4 is divisible by 3.
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HOPE YOU WILL UNDERSTAND MY WORDS, a request is here please as I am an ACE ranker I wish that to make my way easy for the GENIUS rank you should mark my answer brainlest if you wish then only ☺.
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