Taking the divisor as 6, every positive odd integer can be written in the form:

Dividing by 6 leaves one of the remainders 0, 1, 2, 3, 4, 5, so every integer is $6q,6q+1$, …, $6q+5$. The forms $6q,6q+2$ and $6q+4$ are all even, so an odd integer must be $6q+1,6q+3$ or $6q+5$.