Question

Show that any positive odd integer is of the form 4q+1 or 4q+ 3 , where q is some integer​

Answer 1

Answer:

a=bq+r where r = 0,1,2,3

Step-by-step explanation:

Now. a=bq+r

a= 4q +r

r=0

a=4q+0

2.a=bq+r

a=4q+r

a=4q+1

is the odd postive integer

Like this if substitute till 3

You will get answer..

Hope this may help you..

Answer 2

Answer:

Hi

Step-by-step explanation:

Let a be the positive integer

And,b=4

Then by euclid's division lemma,

We can write a=4q+r,for some interger q and 0≤r<4.

Then,possible values of r is 0,1,2,3

Taking r=0

a=4q

taking r=1

a=4q+1

taking r=2

a=4q+2

taking r=3

a=4q+3

But a is an odd positive integer,so a can't be 4q 04 4q+2[as these are         even]

∴a can be of the form 4q+1 or 4q+3 for some integer q.

∴Please mark it as brainlist answer