Question

Let ( a ) be positive odd integer. By division algorithm
[
a=6 times q+r ; 0 leq r<6
]
( Rightarrow a=6 q+0, ) or ( 6 q+1 )
or ( quad 6 q+2, ) or ( 6 q+3 )
or ( quad 6 q+4, ) or ( 6 q+5 )
We reject ( 6 q+0,6 q+2, ) and ( 6 q+4 ) because they are
even integers.
Hence, the possible form of ( a ) is ( 6 q+1 )
or ( 6 q+3, ) or ( 6 q+5 )

# Show that any positive odd integer is of the from 6q+1, or 69 +3, or 69+5,where q is some integer.

Solution