Solution:
Let’s say that be any arbitrary positive odd integer.
Upon dividing by 6, let be the quotient and be the remainder.
Therefore, by Euclid’s division lemma, we get
, where
As and is an integer, can take values
or or or or or
But or or are multiples of 2, so an even integer whereas is an odd integer)
As a result, any positive odd integer is of the form or or , where is some integer.