Question

show that every positive even integer is of the form 2q and that every positive odd integeris of the form of 2q+1?

Answer 1

Let (a) be any positive and b=2 then by euclids lemma

a=bq+r where b=2 r=0,1

so a=2q. or. a=2q+1

if a is form of 2q it is even and as 2q+1 it is odd