Question

show that only one of the numbers n,n+1 and n+4 is divisible by 3​

Answer 1

Answer:

Step-by-step explanation:

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 are  0,1 and 2

so n may be in the form of 3q,    3q=1,    3q+2

CASE-1

If n=3q

n+1=3q+1

n+4=3q+4

here n is only divisible by 3.

CASE 2

if n = 3q+1

n+1 =3q+2

n+4=3q+5

here any one  is not 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+1,n+4 IS DIVISIBLE BY 3 .