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

Show that any positive odd integer is of the form 6q+1, 6q+3, 6q+5 , w

1.	Show that any positive odd integer is of the form 6q+1, 6q+3, 6q+5 , where q is some integer
Answer» Thank you Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder.according to Euclid’s division lemmaa=bq+ra=6q+rwhere , a=0,1,2,3,4,5then,a=6qora=6q+1ora=6q+2ora=6q+3ora=6q+4ora=6q+5but here,a=6q+1 & a=6q+3 & a=6q+5 are odd.