Question

Show that any positive integers is of the form 3q, 3q+1, 3q+2, where q is some integer

Answer 1

Answer:

Let A be any positive integer,

now, by Euclids Division Lemma,

"a=bq+r"

now, b=3

therefore, 'r' should be  0, 1 or 2                           {B'coz 0<r}

now, when r = 0

then,

a=3q+r

a=3q+0

a=3q

when r = 1

a=3q+r

a=3q+1

when r = 2

a=3q+r

a=3q+2

HENCE PROVED

Answer 2

Answer:

Step-by-step explanation:

   a=bq+r

where r=0,1,2

b=3  

when r=0

            a=3q,even  

when r=1

            a=3q+1, odd

when r=2  

          a=3q+2, even  

so , 3q,3q+1,3q+2 are some integers of q