Question

show that every positive even integer is of the form 2m and that every positive odd integer is of the form​

Answer 1

let a be a positive even integer

and b=2 (a=bq+r)

0<r<b

therefore r=0 and 1

if r=0. a=2q+0 =2q .....1eq

and r=1. a=2q+1 ........2eq

from squaring equation 1

we get ,

(2q)^ = 4q^=2(2q^) =2m

where m = 2q^