let the positive odd integer be a

and b=4

a=bq+r where r is less than b/euclid division lemma/

b=4

therefore r=0,1,2,3,

therefore,a=4q+0

a=4q

a=4q+1

a=4q+2

a=4q+3

odd integer

a=4q+1

a=4q+3