Let s be any positive integer.
On dividing s by 4, let m be the quotient and r be the remainder.
By Euclid’s division lemma,
s = 4m + r, where 0 ≤ r ˂ 4
So we have, s = 4m or s = 4m + 1 or s = 4m + 2 or s = 4m + 3.
Here, 4m, 4m + 2 are multiples of 2, which revert even values to s.
Again, s = 4m + 1 or s = 4m + 3 are odd values of s.
Thus, any positive odd integer is of the form (4m + 1) or (4m + 3) where s is any odd integer.