Question

please prove that I circled in the attached picture​

Answer 1

a=bq+r

Take b=4

Since 0<r<4, r=0,1,2,3

So,a=4q,4q+1,4q+2,4q+3

Clearly, a=4q, 4q+2 are even, as they are divisible by 2 .Therefore a cannot be 4q,4q+2 as a is odd. But 4q+1, 4q+3 are odd, as they are not divisible by 2.