Question

use Euclid's division lemma to show that any positive odd integer is of the form 6q+2,or 6q+3 or 6q+5, where q is some integer.​

Answer 1

Use Euclid's division lemma to show that any positive odd integer is of the form 6q+1,6q+3,6q+5 where q is a certain integer.

Answer:-

Let a be a positive odd integer

a=bq+r

b=6

a=6q+r, 0≤r<6. So,the possible values of r are 0,1,2,3,4,5

Set of positive odd integers are {1,3,5,7,9......}

put a=1,3,5,7,9......

a=bq+r

1=6(0)+1=6q+1 [r=1]

3=6(0)+3=6q+3 [r=3]

5=6(0)+5=6q+5 [r=5]

7=6(1)+1=6q+1 [r=1]

9=6(1)+3=6q+3 [r=3]

So,any positive integer is of the form 6q+1,6q+3,6q+5 where q is certain integer.

Answer 2

Answer:

Let a be a positive odd integer

Step-by-step explanation:

A=bq+r , b=6, a=6q+r, 0<_r<b so the possible values of R =0,1,2,3,4,5