Question

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

Answer 1

hii friend!

Given numbers,
n,n+2 and n+4

n is any positive integer.

If n = 1,
n = 1
n+2 = 1+2 = 3 is divisible by 3
n+4 = 1+4 = 5

If n = 2,
n = 2
n+2 = 2+2 = 4
n+4 = 2+4 = 6 is divisible by 3

If n = 3,
n = 3 is divisible by 3
n+2 = 3+2 = 5
n+4 = 3+4 = 7

Therefore, one and only one out of n, n+2 and n+4 is divisible by 3 for any positive integer n.

Answer 2

Hey... I think this can be ur answer!!

Let n =bq +r
b=3
So now,

Case 1

n=3q..

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

Case 2

n=3q+1..

n=3q+1 is not divisible by 3

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

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

Case 3

n=3q+2..

n=3q+2 is not divisible by 3

n+2=3q+2+2
=3q+4 is not divisible by 3

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

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

Hence proved

Hope it helps you dear ☺️☺️