(Q12).Show that every positive odd integer is of the form 6q + 1 or 6q + 3, or 6q+5 where q is some integer.?

Let a be any positive integer

Let b = 6

By dividing algorithm rule for a and b : a = 6q + r, for q > 0,and 0 ≤ r <

The possible remainders are 0, 1, , , ,

So, a = 6q , 6q+1, 6q+2, 6q+3, where q is the

However, since a is

a cannot be 6q = 2(3q) or 6q+2 = 2(3q+1), since they were divisible by

Therefore, any odd integer is of the form 6q + or 6q + or 6q +