Question

Show that one and only one out of n, n + 2 or n + 4 is divisible by 3. Where n is any positive
integer

Answer 1

Answer:

answer is the n , n + 2 or n + 4 is divisible by 3.

where n is any not positive integer

Answer 2

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

$\underline{CASE-1}$

IF N=3q

n+4=3q+4

n+2=3q+2

here n is only divisible by 3

$\underline{CASE-2}$

if n = 3q+1

n+4=3q+5

n+2=3q=3

here only n+2 is divisible by 3

$\underline{CASE-3}$

IF n=3q+2

n+2=3q+4

n+4=3q+2+4

=3q+6

here only n+4 is divisible by 3

HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE