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

1.	Show that any positive odd integer is of the form 6q +1,or 6q +3 or 6q +5 where q is some integer
Answer» LET a be a given integer. By Euclid's DIVISION Lemma a = 6q + r r = 0, 1, 2, 3, 4, 5 When r = 0 $a = 6q \\a = 2(2q)$ Since it is divisible by 2 it is an even number. When r = 1 $a = 6q + 1$ Odd number When r = 2 $a = 6q + 2\\a = 2(2q+1)$ Since it is divisible by 2 it is an even number. When r = 3 $a=6q + 3$ Odd number When r = 4 $a=6q + 4\\a=2(3q+2)$ Since it is divisible by 2 it is an even number. When r = 5 $a= 6q + 5$ Odd number $\boxed{\boxed{\bold{Therefore, \ any \ positive \ odd \ integer \ is \ of \ the \ form \ 6q+1, \6q+3 \ or \ 6q+5. }}}}}}}$