Question

show that one and only
one of n, n+2, n+4 is
divisible by 3 where" m" is some integer. ​

Answer 1

case I: if n =3m

n is divisible by 3,

n+2 = 3m+2 is not divisible by 3.

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

case II: if n =3m+1

n = 3m+1 is not divisible by 3.

n+2 = 3m+1+2=3m+3 = 3(m+1) is divisible by 3.

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

case III: if n = 3m+2

n =3m+2 is not divisible by 3.

n+2 = 3m+2+2 =3q+4 = 3(m+1)+1 is not divisible by 3.

n+4 = 3m+2+4 = 3m+6 = 3(m+2) is divisible by 3.

thus one and only one out of n , n+2, n+4 is divisible by 3.

hope it helps