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Show that one and only one out of n,n+2,n+4 is divisible by 3, where n is any positive integer
Asked by tusharjainrekha12345 | 06 Apr, 2019, 11:48: PM
answered-by-expert Expert Answer
if n is divisible by 3 it can be written as n= 3p, where p is an integer.
 
hence n+2 = 3p+2   and 3p+2 will give remainder 2 when it is divided by 3 . Hence n+2 is not divisble by 3
 
Similarly n+4 = 3p+4 =3(p+1)+ 1.  Hence 3p+4 will give remainder 1 when it is divided by 3 because p+1 is also an integer.
Hence n+4 ia also not divisible by 3
 
It can be concluded that if a number n is divisible by 3 then if multiples of 2 is added to n, then the resulting number will not be divided by 3
Answered by Thiyagarajan K | 07 Apr, 2019, 09:30: AM

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