Question

Use euclid's division Lemma to show every positive integer is either even or odd

Answer 1

a=bq+r (where 0》r)
let a =3
we get...a=3q+ r (where 0》r)
let r=0;1;2

we get....a=3q; 3q+1;3q+2

a=3q ........odd
a=3q+1.......even
a=3q+2.......odd

proved...