Let a is a positive odd integer and apply Euclid’s division algorithm
a = 6q + r, Where 0 ≤ r < 6
for 0 ≤ r < 6 probable remainders are 0, 1, 2, 3, 4 and 5.
a = 6q + 0
or a = 6q + 1
or a = 6q + 2
or a = 6q + 3
or a = 6q + 4
or a = 6q + 5 may be form
Where q is quotient and a = odd integer.
This cannot be in the form of 6q, 6q + 2, 6q + 4.
[all divides by 2]
Hence, any positive odd integer is of the form 6q + 1, or 6q + 3 or (6q + 5)
