Question

Show that any positive odd integer is of the form 6 q + 1 or 6 q + 3 where q is a positive integer​

Answer 1

Let a be any positive odd integer and b=6 by division Lemma There q is a integer

a=6q+r. where 0<r<6

Then r=0,1,2,3,4,5

a=6q, a=6q+1, a=6q+2, a=6q+3,

a=6q+4

a=6q+1, a=6q+3{odd integer}

Hence any positive integer is form 6q+1, 6q+3.