Question

show that one and only one out of n, (n+1) and (n+2) is divisible by 3 , where n is any positive integer​

Answer 1

Answer:

On dividing n by 3, let q be the quotient and r be the remainder . Case I If n = 3q then n is clearly divisible by 3. Case II If n= ( 3q +1) then ( n+2) = (3q +3) = 3(q +1) , which is clearly divisible by 3. Hence, one and only one out of n,( n +1) and (n+2) is divisible by 3.