Show that any positive odd integer is of the form `6q+1` or `6q+3` or `6q+5` , where q is some integer.

Explanation

Let 'a' be any positive odd integer and 'b' =6
Therefore,
`a=6q +r " "0 le r lt 6`
when r=0
`:.`a=6q=2(3q) which is even.
When r=1,
`:.` a =6q+1 =2 (3q)+1 i.e., even +1=odd
when r=2
`:.` a=6q +2 =2(3q+1) , which is even
when r=3
`:.` a=6q +3 =2 (3q+1) + 1i.e., even +1 =odd
When r=4
`:.` a=6q +4 =2(3q+2) , which is even.
When r=5
`:.` a=6q+5=2(3q +2) + 1 i.e., even +1=odd
So se can say that 6q+1 or 6q + 3 or 6q +5 are the forms of any positive odd integers.