Question

show that only one of every three consecutive postive integers is divisible by 3 .

fast i need the answer very urgent !

Answer 1

Answer:

Step-by-step explanation:

let the no .be  (n-1,n,n+1,)

b=3 r = 0,1,2

a=bq+r (bq=n)

case 1 n-1

a= 3q-1                    [r=0]

a= 3q+1-1=3q=3m     [r=1] [q=m][divisible by 3]

a=3q+2-1=3q-1             [r=2]

case 2 n

a=3q=3m             [r=0]     [m=q][divisible by 3]

a=3q+1      [r=1]

a=3q+2    [r=2]

case3 n+1

a= 3q+1               [r=0]

a=3q+1+1=3q+2      [r=1]

a=3q+2+1=3q+3=3(q+1)=3m   [r=2]   [m=q+1][divisible by 3]