Let a is any positive odd integer and b = 4.
Applying Euclid division lemma in a, b
Where o ≤ r < 4 and q is any integer.
r = 0, 1, 2, 3 put
a = 4q + 0
⇒ a = 4q
a = 4q + 1
a = 4q + 2
a = 4q + 4
For positive odd integer.
a ≠ 4 q, a ≠ 4q + 2
Hence, any odd integer is of the form 4q + 1, or 4q + 3.