Question

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

Answer 1

By Euclid Division Lemma

Let a be any positive integer then b = 4

Case 1 r = 2

a = bq + r ( 0<r<b )

a = 4q+1

Case 2. r = 3

a= bq + r ( 0<r<b )

a= 4q + 3

Hence proved