Question

show that any positive odd integer is of the form 4q +1 and 4q + 3 where q is some integer

Answer 1

Let a be any positive integer
by EDL a = bq +r
0 ≤ r < b
possible 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 even
so a ill be in the form of 4q + 1 or 4q+3
hence proved



HOPE THIS WILL BE HELPFUL !!!!!!