Question

show that one and one of n n+2 n+3 is divisible by where n is any positive integer​

Answer 1

Step-by-step explanation:

Question:-Show that any one of n,n+2,n+4 is divisible by 3 where n is any positive integer.

Let n be any positive integer

Let n=3q+r where r={0,1,2}

So possibilities of n are 3q,3q+1,3q+2

Case 1:- If n=3q

n=3q ; n+2=3q+2 ; n+4=3q+4

n is divisible by 3

Case 2:- If n=3q+1

n=3q+1 ; n+2=3q+3=3(q+1) ; n+4=3q+5

n+2 is divisible by 3

Case 3:- If n=3q+2

n=3q+2 ; n+2=3q+4 ; n+4=3q+6=3(q+2)

n+4 is divisible by 3