Question

show that every positive odd integer is of the form 2 q + 1 where Q is some whole number

Answer 1

Dear student, following is the answer to your query:

Let a be any positive integer and b = 2.

Applying Euclid’s algorithm, we have:

a = 2q + r, for some integer q ≥ 0, and 0 ≤ r < 2

a = 2q or 2q + 1

If a = 2q, then a is an even integer.

Now, a positive integer can either be even or odd. Thus, any positive odd integer is of the form 2q + 1.