Question

^Answer the question from the attachment^

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Answer 1

By Euclid's division lemma
a = bq + r , 0 < r < b

Let a be any positive integer
and b = 6
then r = 0 , 1 , 2 , 3 , 4 , 5

When r = 0
a = 6q

When r = 1
a = 6q + 1

When r = 2
a = 6q + 2

When r = 3
a = 6q + 3

When r = 4
a = 6q + 4

When r = 5
a = 6q + 5

(6q) , (6q + 2) , (6q + 4) are even Integers as sum of two even Integers is always even .
So the odd positive Integers are
(6q + 1), (6q + 3) and (6q + 5)

Answer 2

Hey friend , Harish here.

Here is your answer.

To prove ,
 
An odd integer is of the form 6q + 1 , 6 q +3 , 6q + 5 

Proof,

Use Euclid's Division lemma.

It tell us that, a = b q + r , where 0 ≤ r < 8.

Here ,

→  a = 6 q + r   , where 0 ≤ r < 6.

So,

r must be odd, and less than 6 in this condition.

So,

a = 6q + 1 , a = 6q + 3 , a = 6q + 5 . 

Hence proved.
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Hope my answer is helpful to you.