Question

prove that one and only one out of n, n+1, n+2
is divisible by 3 where n is a positive
integer​

Answer 1

Step-by-step explanation:

n,n+1,n+2 are consecutive no.s

n can be one of these forms, 3p, 3p+1 or 3p+2

case 1: n=3p

In this case n is divisible by 3, but n+1, n+2 are not

case 2: n =3p+1

In this case ,n is not divisible, n+1=3p+1+1=3p+2 is not divisible by 3

n+2 =3p+1+2=3p+3=3(p+1) is divisible by 3

case 3: n = 3p+2

n is not divisible by 3

n+1 = 3p+2+1 =3p+3 =3(p+1) is divisible by 3

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

in any case n or n+1, or n+2 is divisible by 3