Question

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

Answer 1

In the place of 'm' u can take 'q'

Answer 2

To Show :

Any positive integer is of the form 3q or 3q+1 or 3q+2 .

Solution :

Let a be any positive integer .

Then b = 3

So by Euclid's Division lemma there exist integers q and r such that ,

a = bq+r

a = 3q+r (b = 3)

And now ,

As we know that according to Euclid's Division Lemma :

0 ≤ r < b

Here ,

0 ≤ r < 3

Here the possible values of r are = 0,1,2

=> 0 ≤ r < 1<2

=> r = 0 or r = 1 or r = 2

And then

a = 3q+r

a = 3q+0 = 3q

a = 3q+1

a = 3q+2

#Hence Proved !!