Question

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

Answer 1

Answer:

yes n is positive integer

Answer 2

Given : one and only one out of n, n + 2 or n + 4 is divisible by 3,

To Find :  Show that

Solution:

Without losing generality

Let say n = 3k , 3k+ 1 , 3k+ 2

n  = 3k      is Divisible by 3

n + 2 = 3k + 2  is not divisible by  3

n + 4 = 3k + 4 = 3(k + 1)  + 1    is not divisible by  3

only one is divisible

n = 3k + 1  is not divisible by  3

n + 2 = 3k + 1 + 2 = 3k + 3 = 3(k +1 )   is Divisible by 3

n + 4 = 3k + 1 + 4 = 3k + 5 = 3(k + 1) + 2      is not divisible by  3

only one is divisible

n = 3k + 2   is not divisible by  3

n + 2 = 3k + 2 + 2 = 3k + 4  =  3(k + 1)  + 1    is not divisible by  3

n + 4 = 3k + 2 + 4 = 3k + 6 = 3(k + 2)     is Divisible by 3

only one is divisible

Hence We can say that one and only one out of n, n + 2 or n + 4 is divisible by 3,

Learn More:

Prove that only one of the numbers n-1, n+1 or n+3 is divisible by 3 ...

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