Question

Show that every odd integer is of the form (4q + 1) or (4q + 3), where q is some integer

Answer 1

Answer:

let a=bq+r .....(1)

let b =4 where r =0,1,2,3

put r=0 in eq 1 and b =4

a=4q+0

a =4q

put r =1

a =4q+1

put r =2

a=4q+2

put r =3

a=4q+3

4q,4q+1,4q+2,4q+3....

odd no.obtained ...4q+1,4q+3..