Question

Show that every even positive integer is of the form 2m and every odd integer is inthe form 2m+1 where m is some integer

Answer 1

Answer:

Let, a be any positive integer and b=2. Using Euclid's lemma,we get: a=2m+r where 0<or =r<2 and q is some integer.

Therefore, a=2m or a=2m+1

Hence, 2m is an even positive integer, since, it is divisible by 2 whereas 2m+1 is an odd integer as it is not divisible by 2.

Answer 2

Yes. all even positive integers are of the form  2m.    where m = integer.

all odd integers are of the form   2m+1