Question

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Q. Show that any positive odd integer is of the form (6p+1), (6p+3) or (6p+5), where p is some integer​

Answer 1

Answer:

hope this attachment will help you...

Answer 2

Step-by-step explanation:

Let n be a given positive odd integer.

On dividing n by 6 , let Q be the Quotient and r be the reminder.

Then , by Euclid's division lemma , we have

=> N = 6Q+r , Where r = 0,1,2,3,4,5

=> N = 6Q or (6Q+1) or (6Q+2) or (6Q+3) or (6Q+4) or (6Q+5) .

But , N = 6Q , (6Q+2) , (6Q+4) are the even values of n.

Thus, when n is odd, it is in the form of (6Q+1) or (6Q+3) or (6Q+5) for some integer Q.