Question
Wed June 06, 2012 By: Ankit Rao
 

show that only one of the number n,n+2 & n+4 is divisible by 3.

Expert Reply
Wed June 06, 2012

CASE I. Let n be of the form 3m

 

then n is divisible by 3 where as n+2, n+4 are not

 

CASE II. Let n be of the form 3m+1

then n+2 = 3(m+1) = 3k which is divisible by 3

n and n+4 are not divisible by 3

 

CASE III. n = 3m+2

=> n+4 = 3m+6 = 3(m+2) = 3x which is divisible by 3

but n, n+2 are not divisible by 3

 

Hence only one out of n, n+2, n+4 is divisible by 3, where n is an integer

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