Question

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

Answer 1

Hey!!

Here is your answer ➡

let n be any positive integer and b=3
n =3q+r
where q is the quotient and r is the remainder
0_ <r<3
so the remainders may be 0,1 and 2
so n may be in the form of 3q, 3q=1,3q+2

CASE-1

IF N=3q
n+4=3q+4
n+2=3q+2
here n is only divisible by 3

CASE 2

if n = 3q+1
n+4=3q+5
n+2=3q=3
here only n+2 is divisible by 3

CASE 3

IF n=3q+2
n+2=3q+4
n+4=3q+2+4
=3q+6
here only n+4 is divisible by 3

And so only one out of n (n+1) and (n+2) is divisible bye 3.
_________________________

Hope it helps ^_^

Answer 2

n= 3q
n=3q+1
n=3q+2

1) n (n+1)
3q (3q +1)
9q^2 +3q
3q (3q +1)
3m. where m= q (3q+1)