Question

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

Answer 1

Answer:

Step-by-step explanation:

Solution:

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

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

Answer 2

Answer:

let n

case 1

is divisible by 3

b=3

r=0,1,2

a=3b

a=3b+1

a=3b+2

case 2

let n+1 is divisible by 3

similar

a=3 (n+1)

a=3 (n+1)+1

a=3 (n+1)+2

Case 3

let n+2 is divisible by 3

similar

a=3 (n+2)

a=3 (n+2)+1

a=3 (n+2)+2

one and only one is divisible by 3