Question

Show that every positive add integers is of the form (4q+1) or (4q+3) for some integer q.

Answer 1

let a be any positive integer by EDL  a = bq +r 0 ≤ r < bpossible remainders are 0, 1, 2 , 3  this shows that a can be in the form of 4q, 4q+1, 4q+2, 4q+3 q is quotient as a is odd a  can't be the form of 4q or 4q+2 as they are evenso a ill be in the form of 4q + 1 or 4q+3 hence proved i hope this will help you