Question

prove that the same of any positive in integar is of the from 4q or 4q+1 for same integar q

Answer 1

let a be any positive integer and b=4 , so it can be written by Euclid division lemma as a=bq+r where r = 0, 1, 2, 3
case 1 --> a = 4q + 0
a = 4q
case 2 --> a = 4q +1

hence for some positive integer q is of form 4q or 4q+1