Question

Prove that if x and y are 2 odd positive integer is of the form 2q+1 for some integer

Answer 1

let 'a' be any positive integer and b=2

By euclid's division algorithm

a=bq+r       0≤r<b

a=2q+r       0≤r<2

(i.e) r =0,1

r=0 , a=2q+0=> a=2q

r=1, a=2q+1

if a is the form of 2m then 'a' is an even integer and positive odd integer is of the form 2m+1