Question

show that one and only out of n,n+3,n+6,n+9(n€N) is divisible by 4

Answer 1

let n be any positive integer and b=4.then by euclid's  division lemma,x=4q+r.

positive remainders are 0,1,2and 3,since 0<=r<4.then x can be 4q/4q+1/4q+2/4q+3.

1. n=4q,it is divisible by 4

2. n=4q+1,  n+3=4q+1+3=4q+4

  =4(q+1),it is divisible by 4

3. n=4q+2,       n+6=4q+2+6

                                  =4q+8

                                  =4(q+2),it is divisible by 4

4. n=4q+3,         n+9=4q+3+9

                                    =4q+12

                                    =4(q+3) ,it is divisible by 4

therefore one and only one out of n,n+1,n+2,n+3 is divisible by 4

  i hope its helpful