Question

show that every positive even integer is of the form 2q and that every positive odd integer is if the form 2q + 1 where q is some integer

Answer 1

Answer:

Step-by-step explanation:

Let any positive (even/odd) integer be a.

By Euclid's Lemma we know that,

Vol 89

a = 2q + r where, 0<r<2

Here, r can be equal or greater than zero but less than 2 at any cost.

This possible values for r can be 0 or 1.

r = 0 and 1

By substituting values of r,

a = 2q and a = 2q + 1

Thus, a will be an even positive integer for 2q.

Similarily, a will be an odd positive integer for 2q + 1.