Question

SHOW THAT ANY POSITIVE ODD INTEGER IS OF THE FORM 4 Q +1 OR 4Q+3 . WHERE Q IS SOME INTEGER ??

Answer 1

there's the answer of the question

Answer 2

Let us take a as any positive integer and b = 4.

By applying Euclid's Divisio Lemms, we get

a = bq + r (r is remainder and r = 0,1,2,3, 0 <= r < b, q>=0)

Therefore, the total possible forms = 4q + 0, 4q + 1, 4q + 2, 4q + 3.

Now,

(1)

= > 4Q + 0 = (It is divisible by 2 - Even number).

(2)

= > 4Q + 1 = (1 is not divisible by 2 - Odd number)


(3)

4Q + 2 = (2 is divisible by 2 - Even number)


(4)

4Q + 3 = (3 is not divisible by 2 - Odd number)


Therefore,

4Q + 1, 4Q + 3 are the positive odd integers.



Hope this helps!