Question

Show that any positive add integer is of the form 4q +1 or 4q+3,
q is some integer.​

Answer 1

Let a be any postive odd integer and b = 4. And b divides a forming quotient and remainder q and r respectively.

∴ a = 4q + r (where 0 ≤ r < b)

⇒ r can be 0, 1, 2, and 3.

So, any postive odd integer is in the form of (4q + 1) and (4q + 3) where q is some integer (as 2 divides 4q and 4q + 2).

NB: Select the correct subject.