Question

Use euclid division lemma to show that any odd positive integer is of the form 6q+1, 6q+3,6q+5 where q is some integers

Answer 1

Hii friend,

Let n be a given positive of integer .

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

Then, by Euclid division lemma , we have:

=> n = 6Q + r, where r = 0 , 1 , 2 , 3 , 4 , 5

When R = 0

N = 6Q

When R = 1

Then,

N = 6Q+1

When R = 2

N = 6Q+2

When R = 3

N = 6Q+3

When R = 4

N = 6Q+4

When R = 5

N= 6Q+5

Clearly,

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

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) , (6Q+3) (6Q+5) for some integer Q.

HOPE IT WILL HELP YOU..... :-)

Answer 2

••Hey user ••

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